Theorem fveq12i 5473

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 5468	. 2 |- ( F ` A ) = ( G ` A )
3		fveq12i.2	. . 3 |- A = B
4	3	fveq2i 5470	. 2 |- ( G ` A ) = ( G ` B )
5	2, 4	eqtri 2178	1 |- ( F ` A ) = ( G ` B )

Syntax hints:   = wceq 1335   ` cfv 5169

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-v 2714  df-un 3106  df-sn 3566  df-pr 3567  df-op 3569  df-uni 3773  df-br 3966  df-iota 5134  df-fv 5177

This theorem is referenced by: (None)