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Theorem ereq1 6914
 Description: Equality theorem for equivalence predicate. (Contributed by NM, 4-Jun-1995.) (Revised by Mario Carneiro, 12-Aug-2015.)
Assertion
Ref Expression
ereq1

Proof of Theorem ereq1
StepHypRef Expression
1 releq 4961 . . 3
2 dmeq 5072 . . . 4
32eqeq1d 2446 . . 3
4 cnveq 5048 . . . . . 6
5 coeq1 5032 . . . . . . 7
6 coeq2 5033 . . . . . . 7
75, 6eqtrd 2470 . . . . . 6
84, 7uneq12d 3504 . . . . 5
98sseq1d 3377 . . . 4
10 sseq2 3372 . . . 4
119, 10bitrd 246 . . 3
121, 3, 113anbi123d 1255 . 2
13 df-er 6907 . 2
14 df-er 6907 . 2
1512, 13, 143bitr4g 281 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   w3a 937   wceq 1653   cun 3320   wss 3322  ccnv 4879   cdm 4880   ccom 4884   wrel 4885   wer 6904 This theorem is referenced by:  riiner  6979  efglem  15350  efger  15352  efgrelexlemb  15384  efgcpbllemb  15389  frgpuplem  15406  pstmxmet  24294 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215  df-opab 4269  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-er 6907
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