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Mirrors > Home > MPE Home > Th. List > infxpenc2lem3OLD | Unicode version |
Description: Lemma for infxpenc2OLD 8424. (Contributed by Mario Carneiro, 30-May-2015.) Obsolete version of infxpenc2lem3 8419 as of 7-Jul-2019. (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
infxpenc2OLD.1 | |
infxpenc2OLD.2 | |
infxpenc2OLD.3 | |
infxpenc2OLD.4 | |
infxpenc2OLD.5 |
Ref | Expression |
---|---|
infxpenc2lem3OLD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | infxpenc2OLD.1 | . 2 | |
2 | infxpenc2OLD.2 | . 2 | |
3 | infxpenc2OLD.3 | . 2 | |
4 | infxpenc2OLD.4 | . 2 | |
5 | infxpenc2OLD.5 | . 2 | |
6 | eqid 2457 | . 2 | |
7 | eqid 2457 | . 2 | |
8 | eqid 2457 | . 2 | |
9 | eqid 2457 | . 2 | |
10 | eqid 2457 | . 2 | |
11 | eqid 2457 | . 2 | |
12 | eqid 2457 | . 2 | |
13 | eqid 2457 | . 2 | |
14 | eqid 2457 | . 2 | |
15 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 | infxpenc2lem2OLD 8422 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -> wi 4 = wceq 1395
E. wex 1612 e. wcel 1818 A. wral 2807
E. wrex 2808 { crab 2811 cvv 3109
\ cdif 3472 C_ wss 3475 c0 3784 <. cop 4035 e. cmpt 4510
cid 4795
con0 4883 X. cxp 5002 `' ccnv 5003
ran crn 5005 |` cres 5006 " cima 5007
o. ccom 5008 -1-1-onto-> wf1o 5592 ` cfv 5593 (class class class)co 6296
e. cmpt2 6298 com 6700
c1o 7142
c2o 7143
coa 7146
comu 7147
coe 7148
cmap 7439
cfn 7536 ccnf 8099 |
This theorem is referenced by: infxpenc2OLD 8424 |
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-rep 4563 ax-sep 4573 ax-nul 4581 ax-pow 4630 ax-pr 4691 ax-un 6592 ax-inf2 8079 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 974 df-3an 975 df-tru 1398 df-fal 1401 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-reu 2814 df-rmo 2815 df-rab 2816 df-v 3111 df-sbc 3328 df-csb 3435 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-iun 4332 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-se 4844 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-isom 5602 df-riota 6257 df-ov 6299 df-oprab 6300 df-mpt2 6301 df-om 6701 df-1st 6800 df-2nd 6801 df-supp 6919 df-recs 7061 df-rdg 7095 df-seqom 7132 df-1o 7149 df-2o 7150 df-oadd 7153 df-omul 7154 df-oexp 7155 df-er 7330 df-map 7441 df-en 7537 df-dom 7538 df-sdom 7539 df-fin 7540 df-fsupp 7850 df-oi 7956 df-cnf 8100 |
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