Theorem fveq12i 6651

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 6646	. 2 ⊢ (𝐹‘𝐴) = (𝐺‘𝐴)
3		fveq12i.2	. . 3 ⊢ 𝐴 = 𝐵
4	3	fveq2i 6648	. 2 ⊢ (𝐺‘𝐴) = (𝐺‘𝐵)
5	2, 4	eqtri 2821	1 ⊢ (𝐹‘𝐴) = (𝐺‘𝐵)

Syntax hints:   = wceq 1538  ‘cfv 6324

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-un 3886  df-in 3888  df-ss 3898  df-sn 4526  df-pr 4528  df-op 4532  df-uni 4801  df-br 5031  df-iota 6283  df-fv 6332

This theorem is referenced by:  cats1fvn  14211  sadcadd  15797  sadadd2  15799  coe1fzgsumdlem  20930  evl1gsumdlem  20980  madufval  21242  clwlkcompbp  27571  2wlkond  27723  1pthond  27929  3cycld  27963  2cycld  32498  kur14lem5  32570  bj-ndxarg  34492  fourierdlem62  42810  fouriersw  42873  ackval41a  45108  ackval42  45110