Mathbox for Alexander van der Vekens < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  afveq12d Structured version   Unicode version

Theorem afveq12d 27975
 Description: Equality deduction for function value, analogous to fveq12d 5736. (Contributed by Alexander van der Vekens, 26-May-2017.)
Hypotheses
Ref Expression
afveq12d.1
afveq12d.2
Assertion
Ref Expression
afveq12d ''' '''

Proof of Theorem afveq12d
StepHypRef Expression
1 afveq12d.1 . . . 4
2 afveq12d.2 . . . 4
31, 2dfateq12d 27971 . . 3 defAt defAt
41, 2fveq12d 5736 . . 3
5 eqidd 2439 . . 3
63, 4, 5ifbieq12d 3763 . 2 defAt defAt
7 dfafv2 27974 . 2 ''' defAt
8 dfafv2 27974 . 2 ''' defAt
96, 7, 83eqtr4g 2495 1 ''' '''
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653  cvv 2958  cif 3741  cfv 5456   defAt wdfat 27949  '''cafv 27950 This theorem is referenced by:  afveq1  27976  afveq2  27977  csbafv12g  27979  afvco2  28018  aoveq123d  28020 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-rex 2713  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-uni 4018  df-br 4215  df-opab 4269  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-res 4892  df-iota 5420  df-fun 5458  df-fv 5464  df-dfat 27952  df-afv 27953
 Copyright terms: Public domain W3C validator