Theorem fveq12i 6887

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 6882	. 2 ⊢ (𝐹‘𝐴) = (𝐺‘𝐴)
3		fveq12i.2	. . 3 ⊢ 𝐴 = 𝐵
4	3	fveq2i 6884	. 2 ⊢ (𝐺‘𝐴) = (𝐺‘𝐵)
5	2, 4	eqtri 2752	1 ⊢ (𝐹‘𝐴) = (𝐺‘𝐵)

Syntax hints:   = wceq 1533  ‘cfv 6533

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-rab 3425  df-v 3468  df-dif 3943  df-un 3945  df-in 3947  df-ss 3957  df-nul 4315  df-if 4521  df-sn 4621  df-pr 4623  df-op 4627  df-uni 4900  df-br 5139  df-iota 6485  df-fv 6541

This theorem is referenced by:  cats1fvn  14805  sadcadd  16395  sadadd2  16397  coe1fzgsumdlem  22135  evl1gsumdlem  22185  madufval  22449  clwlkcompbp  29463  2wlkond  29615  1pthond  29821  3cycld  29855  2cycld  34584  kur14lem5  34656  bj-ndxarg  36414  fourierdlem62  45335  fouriersw  45398  ackval41a  47534  ackval42  47536