Theorem fveq12i 6899

Description: Equality deduction for function value. (Contributed by FL, 27-Jun-2014.)

Hypotheses

Ref	Expression
fveq12i.1	⊢ 𝐹 = 𝐺
fveq12i.2	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
fveq12i	⊢ (𝐹‘𝐴) = (𝐺‘𝐵)

Proof of Theorem fveq12i

Step	Hyp	Ref	Expression
1		fveq12i.1	. . 3 ⊢ 𝐹 = 𝐺
2	1	fveq1i 6894	. 2 ⊢ (𝐹‘𝐴) = (𝐺‘𝐴)
3		fveq12i.2	. . 3 ⊢ 𝐴 = 𝐵
4	3	fveq2i 6896	. 2 ⊢ (𝐺‘𝐴) = (𝐺‘𝐵)
5	2, 4	eqtri 2786	1 ⊢ (𝐹‘𝐴) = (𝐺‘𝐵)

This proof depends on syntax axioms:   = wceq 1569  ‘cfv 6546

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2101  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3416  df-v 3455  df-ss 3900  df-dif 4049  df-un 4153  df-nul 4281  df-if 4485  df-sn 4588  df-pr 4590  df-op 4838  df-uni 4870  df-br 5106  df-iota 6500  df-fv 6554

This theorem is used by:  cats1fvn  15020  sadcadd  16640  sadadd2  16642  coe1fzgsumdlem  22633  evl1gsumdlem  22686  madufval  22964  clwlkcompbp  30381  2wlkond  30538  1pthond  30747  2cycld  30757  3cycld  30791  kur14lem5  36096  bj-ndxarg  38137  evl1gprodd  43307  aks5lem3a  43379  fourierdlem62  47317  fouriersw  47380  ackval41a  49945  ackval42  49947  fuconuniqlem  50920  fuconuniqvalslem  50922