Theorem fveq12i 5427

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 5422	. 2 |- ( F ` A ) = ( G ` A )
3		fveq12i.2	. . 3 |- A = B
4	3	fveq2i 5424	. 2 |- ( G ` A ) = ( G ` B )
5	2, 4	eqtri 2160	1 |- ( F ` A ) = ( G ` B )

Syntax hints:   = wceq 1331   ` cfv 5123

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-iota 5088  df-fv 5131

This theorem is referenced by: (None)