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Mirrors > Home > MPE Home > Th. List > isf32lem5 | Unicode version |
Description: Lemma for isfin3-2 8768. There are infinite decrease points. (Contributed by Stefan O'Rear, 5-Nov-2014.) |
Ref | Expression |
---|---|
isf32lem.a | |
isf32lem.b | |
isf32lem.c | |
isf32lem.d |
Ref | Expression |
---|---|
isf32lem5 |
S
,Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isf32lem.a | . . . 4 | |
2 | isf32lem.b | . . . 4 | |
3 | isf32lem.c | . . . 4 | |
4 | 1, 2, 3 | isf32lem2 8755 | . . 3 |
5 | 4 | ralrimiva 2871 | . 2 |
6 | isf32lem.d | . . . . . . . 8 | |
7 | ssrab2 3584 | . . . . . . . 8 | |
8 | 6, 7 | eqsstri 3533 | . . . . . . 7 |
9 | nnunifi 7791 | . . . . . . 7 | |
10 | 8, 9 | mpan 670 | . . . . . 6 |
11 | 10 | adantl 466 | . . . . 5 |
12 | elssuni 4279 | . . . . . . . . . . . . 13 | |
13 | nnon 6706 | . . . . . . . . . . . . . 14 | |
14 | omsson 6704 | . . . . . . . . . . . . . . 15 | |
15 | 14, 11 | sseldi 3501 | . . . . . . . . . . . . . 14 |
16 | ontri1 4917 | . . . . . . . . . . . . . 14 | |
17 | 13, 15, 16 | syl2anr 478 | . . . . . . . . . . . . 13 |
18 | 12, 17 | syl5ib 219 | . . . . . . . . . . . 12 |
19 | 18 | con2d 115 | . . . . . . . . . . 11 |
20 | 19 | impr 619 | . . . . . . . . . 10 |
21 | 6 | eleq2i 2535 | . . . . . . . . . 10 |
22 | 20, 21 | sylnib 304 | . . . . . . . . 9 |
23 | suceq 4948 | . . . . . . . . . . . . 13 | |
24 | 23 | fveq2d 5875 | . . . . . . . . . . . 12 |
25 | fveq2 5871 | . . . . . . . . . . . 12 | |
26 | 24, 25 | psseq12d 3597 | . . . . . . . . . . 11 |
27 | 26 | elrab3 3258 | . . . . . . . . . 10 |
28 | 27 | ad2antrl 727 | . . . . . . . . 9 |
29 | 22, 28 | mtbid 300 | . . . . . . . 8 |
30 | 29 | expr 615 | . . . . . . 7 |
31 | imnan 422 | . . . . . . 7 | |
32 | 30, 31 | sylib 196 | . . . . . 6 |
33 | 32 | nrexdv 2913 | . . . . 5 |
34 | eleq1 2529 | . . . . . . . . 9 | |
35 | 34 | anbi1d 704 | . . . . . . . 8 |
36 | 35 | rexbidv 2968 | . . . . . . 7 |
37 | 36 | notbid 294 | . . . . . 6 |
38 | 37 | rspcev 3210 | . . . . 5 |
39 | 11, 33, 38 | syl2anc 661 | . . . 4 |
40 | rexnal 2905 | . . . 4 | |
41 | 39, 40 | sylib 196 | . . 3 |
42 | 41 | ex 434 | . 2 |
43 | 5, 42 | mt2d 117 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -. wn 3 -> wi 4
<-> wb 184 /\ wa 369 = wceq 1395
e. wcel 1818 A. wral 2807 E. wrex 2808
{ crab 2811 C_ wss 3475 C. wpss 3476
~P cpw 4012 U. cuni 4249 |^| cint 4286
con0 4883 suc csuc 4885 ran crn 5005
--> wf 5589 ` cfv 5593 com 6700
cfn 7536 |
This theorem is referenced by: isf32lem6 8759 isf32lem7 8760 isf32lem8 8761 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 ax-8 1820 ax-9 1822 ax-10 1837 ax-11 1842 ax-12 1854 ax-13 1999 ax-ext 2435 ax-sep 4573 ax-nul 4581 ax-pow 4630 ax-pr 4691 ax-un 6592 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 974 df-3an 975 df-tru 1398 df-ex 1613 df-nf 1617 df-sb 1740 df-eu 2286 df-mo 2287 df-clab 2443 df-cleq 2449 df-clel 2452 df-nfc 2607 df-ne 2654 df-ral 2812 df-rex 2813 df-rab 2816 df-v 3111 df-sbc 3328 df-dif 3478 df-un 3480 df-in 3482 df-ss 3489 df-pss 3491 df-nul 3785 df-if 3942 df-pw 4014 df-sn 4030 df-pr 4032 df-tp 4034 df-op 4036 df-uni 4250 df-int 4287 df-br 4453 df-opab 4511 df-mpt 4512 df-tr 4546 df-eprel 4796 df-id 4800 df-po 4805 df-so 4806 df-fr 4843 df-we 4845 df-ord 4886 df-on 4887 df-lim 4888 df-suc 4889 df-xp 5010 df-rel 5011 df-cnv 5012 df-co 5013 df-dm 5014 df-rn 5015 df-res 5016 df-ima 5017 df-iota 5556 df-fun 5595 df-fn 5596 df-f 5597 df-f1 5598 df-fo 5599 df-f1o 5600 df-fv 5601 df-om 6701 df-1o 7149 df-er 7330 df-en 7537 df-fin 7540 |
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