Theorem fveq12i 5582

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 5577	. 2 |- ( F ` A ) = ( G ` A )
3		fveq12i.2	. . 3 |- A = B
4	3	fveq2i 5579	. 2 |- ( G ` A ) = ( G ` B )
5	2, 4	eqtri 2226	1 |- ( F ` A ) = ( G ` B )

Syntax hints:   = wceq 1373   ` cfv 5271

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-rex 2490  df-v 2774  df-un 3170  df-sn 3639  df-pr 3640  df-op 3642  df-uni 3851  df-br 4045  df-iota 5232  df-fv 5279

This theorem is referenced by: (None)