Theorem fveq12i 6922

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 6917	. 2 ⊢ (𝐹‘𝐴) = (𝐺‘𝐴)
3		fveq12i.2	. . 3 ⊢ 𝐴 = 𝐵
4	3	fveq2i 6919	. 2 ⊢ (𝐺‘𝐴) = (𝐺‘𝐵)
5	2, 4	eqtri 2786	1 ⊢ (𝐹‘𝐴) = (𝐺‘𝐵)

This proof depends on syntax axioms:   = wceq 1570  ‘cfv 6566

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-v 3456  df-ss 3901  df-dif 4050  df-un 4154  df-nul 4282  df-if 4486  df-sn 4589  df-pr 4591  df-op 4841  df-uni 4873  df-br 5109  df-iota 6520  df-fv 6574

This theorem is used by:  cats1fvn  15051  sadcadd  16672  sadadd2  16674  coe1fzgsumdlem  22676  evl1gsumdlem  22729  madufval  23007  clwlkcompbp  30426  2wlkond  30583  1pthond  30792  2cycld  30802  3cycld  30836  kur14lem5  36183  bj-ndxarg  38268  evl1gprodd  43433  aks5lem3a  43505  fourierdlem62  47451  fouriersw  47514  ackval41a  50137  ackval42  50139  fuconuniqlem  51112  fuconuniqvalslem  51114