Users' Mathboxes Mathbox for Alexander van der Vekens < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  afveq1 Structured version   Visualization version   GIF version

Theorem afveq1 47119
Description: Equality theorem for function value, analogous to fveq1 6903. (Contributed by Alexander van der Vekens, 22-Jul-2017.)
Assertion
Ref Expression
afveq1 (𝐹 = 𝐺 → (𝐹'''𝐴) = (𝐺'''𝐴))

Proof of Theorem afveq1
StepHypRef Expression
1 id 22 . 2 (𝐹 = 𝐺𝐹 = 𝐺)
2 eqidd 2737 . 2 (𝐹 = 𝐺𝐴 = 𝐴)
31, 2afveq12d 47118 1 (𝐹 = 𝐺 → (𝐹'''𝐴) = (𝐺'''𝐴))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1540  '''cafv 47102
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2707  ax-sep 5294  ax-nul 5304  ax-pr 5430
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2539  df-eu 2568  df-clab 2714  df-cleq 2728  df-clel 2815  df-nfc 2891  df-ne 2940  df-ral 3061  df-rex 3070  df-rab 3436  df-v 3481  df-sbc 3788  df-csb 3899  df-dif 3953  df-un 3955  df-in 3957  df-ss 3967  df-nul 4333  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-uni 4906  df-int 4945  df-br 5142  df-opab 5204  df-id 5576  df-xp 5689  df-rel 5690  df-cnv 5691  df-co 5692  df-dm 5693  df-res 5695  df-iota 6512  df-fun 6561  df-fv 6567  df-aiota 47070  df-dfat 47104  df-afv 47105
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator