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 47034
Description: Equality theorem for function value, analogous to fveq1 6900. (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 2734 . 2 (𝐹 = 𝐺𝐴 = 𝐴)
31, 2afveq12d 47033 1 (𝐹 = 𝐺 → (𝐹'''𝐴) = (𝐺'''𝐴))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1535  '''cafv 47017
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1963  ax-7 2003  ax-8 2106  ax-9 2114  ax-10 2137  ax-11 2153  ax-12 2173  ax-ext 2704  ax-sep 5300  ax-nul 5307  ax-pr 5430
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1087  df-tru 1538  df-fal 1548  df-ex 1775  df-nf 1779  df-sb 2061  df-mo 2536  df-eu 2565  df-clab 2711  df-cleq 2725  df-clel 2812  df-nfc 2888  df-ne 2937  df-ral 3058  df-rex 3067  df-rab 3433  df-v 3479  df-sbc 3792  df-csb 3909  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4915  df-int 4954  df-br 5150  df-opab 5212  df-id 5576  df-xp 5689  df-rel 5690  df-cnv 5691  df-co 5692  df-dm 5693  df-res 5695  df-iota 6510  df-fun 6560  df-fv 6566  df-aiota 46985  df-dfat 47019  df-afv 47020
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator