Theorem fveq12i 6885

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 6880	. 2 ⊢ (𝐹‘𝐴) = (𝐺‘𝐴)
3		fveq12i.2	. . 3 ⊢ 𝐴 = 𝐵
4	3	fveq2i 6882	. 2 ⊢ (𝐺‘𝐴) = (𝐺‘𝐵)
5	2, 4	eqtri 2783	1 ⊢ (𝐹‘𝐴) = (𝐺‘𝐵)

This proof depends on syntax axioms:   = wceq 1570  ‘cfv 6533

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

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 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-v 3452  df-dif 3902  df-un 3904  df-ss 3916  df-nul 4280  df-if 4483  df-sn 4585  df-pr 4587  df-op 4591  df-uni 4868  df-br 5104  df-iota 6489  df-fv 6541

This theorem is used by:  cats1fvn  14932  sadcadd  16551  sadadd2  16553  coe1fzgsumdlem  22531  evl1gsumdlem  22584  madufval  22862  clwlkcompbp  30251  2wlkond  30408  1pthond  30617  2cycld  30627  3cycld  30661  kur14lem5  35792  bj-ndxarg  37830  evl1gprodd  42986  aks5lem3a  43058  fourierdlem62  46999  fouriersw  47062  ackval41a  49627  ackval42  49629