Theorem fveq1i 5330

Description: Equality inference for function value. (Contributed by set.mm contributors, 2-Sep-2003.)

Hypothesis

Ref	Expression
fveq1i.1	⊢ F = G

Assertion

Ref	Expression
fveq1i	⊢ (F ‘A) = (G ‘A)

Proof of Theorem fveq1i

Step	Hyp	Ref	Expression
1		fveq1i.1	. 2 ⊢ F = G
2		fveq1 5328	. 2 ⊢ (F = G → (F ‘A) = (G ‘A))
3	1, 2	ax-mp 5	1 ⊢ (F ‘A) = (G ‘A)

Syntax hints:   = wceq 1642   ‘cfv 4782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-rex 2621  df-uni 3893  df-iota 4340  df-br 4641  df-fv 4796

This theorem is referenced by:  fvun2  5381  fvopab3ig  5388  fvsnun1  5448  fvsnun2  5449  fvpr1  5450  fvpr2  5451  f1ocnvfv2  5478  ov  5596  ovigg  5597  ovg  5602  fvfullfun  5865