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Theorem ofreq 6311
 Description: Equality theorem for function relation. (Contributed by Mario Carneiro, 28-Jul-2014.)
Assertion
Ref Expression
ofreq

Proof of Theorem ofreq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 breq 4217 . . . 4
21ralbidv 2727 . . 3
32opabbidv 4274 . 2
4 df-ofr 6309 . 2
5 df-ofr 6309 . 2
63, 4, 53eqtr4g 2495 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653  wral 2707   cin 3321   class class class wbr 4215  copab 4268   cdm 4881  cfv 5457   cofr 6307 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-ral 2712  df-br 4216  df-opab 4270  df-ofr 6309
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