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Theorem ofrval 6550
Description: Exhibit a function relation at a point. (Contributed by Mario Carneiro, 28-Jul-2014.)
Hypotheses
Ref Expression
offval.1
offval.2
offval.3
offval.4
offval.5
ofval.6
ofval.7
Assertion
Ref Expression
ofrval

Proof of Theorem ofrval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 offval.1 . . . . . 6
2 offval.2 . . . . . 6
3 offval.3 . . . . . 6
4 offval.4 . . . . . 6
5 offval.5 . . . . . 6
6 eqidd 2458 . . . . . 6
7 eqidd 2458 . . . . . 6
81, 2, 3, 4, 5, 6, 7ofrfval 6548 . . . . 5
98biimpa 484 . . . 4
10 fveq2 5871 . . . . . 6
11 fveq2 5871 . . . . . 6
1210, 11breq12d 4465 . . . . 5
1312rspccv 3207 . . . 4
149, 13syl 16 . . 3
15143impia 1193 . 2
16 simp1 996 . . 3
17 inss1 3717 . . . . 5
185, 17eqsstr3i 3534 . . . 4
19 simp3 998 . . . 4
2018, 19sseldi 3501 . . 3
21 ofval.6 . . 3
2216, 20, 21syl2anc 661 . 2
23 inss2 3718 . . . . 5
245, 23eqsstr3i 3534 . . . 4
2524, 19sseldi 3501 . . 3
26 ofval.7 . . 3
2716, 25, 26syl2anc 661 . 2
2815, 22, 273brtr3d 4481 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818  A.wral 2807  i^icin 3474   class class class wbr 4452  Fnwfn 5588  `cfv 5593  oRcofr 6539
This theorem is referenced by:  itg1le  22120  gsumle  27770  ftc1anclem5  30094
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-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-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  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-reu 2814  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-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-iun 4332  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  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-ofr 6541
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