Theorem fveq12i 6840

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 6835	. 2 ⊢ (𝐹‘𝐴) = (𝐺‘𝐴)
3		fveq12i.2	. . 3 ⊢ 𝐴 = 𝐵
4	3	fveq2i 6837	. 2 ⊢ (𝐺‘𝐴) = (𝐺‘𝐵)
5	2, 4	eqtri 2759	1 ⊢ (𝐹‘𝐴) = (𝐺‘𝐵)

Syntax hints:   = wceq 1541  ‘cfv 6492

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3400  df-v 3442  df-dif 3904  df-un 3906  df-ss 3918  df-nul 4286  df-if 4480  df-sn 4581  df-pr 4583  df-op 4587  df-uni 4864  df-br 5099  df-iota 6448  df-fv 6500

This theorem is referenced by:  cats1fvn  14781  sadcadd  16385  sadadd2  16387  coe1fzgsumdlem  22247  evl1gsumdlem  22300  madufval  22581  clwlkcompbp  29855  2wlkond  30010  1pthond  30219  3cycld  30253  2cycld  35332  kur14lem5  35404  bj-ndxarg  37282  evl1gprodd  42371  aks5lem3a  42443  fourierdlem62  46412  fouriersw  46475  ackval41a  48940  ackval42  48942