Theorem fveq1d 5331

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

Hypothesis

Ref	Expression
fveq1d.1	⊢ (φ → F = G)

Assertion

Ref	Expression
fveq1d	⊢ (φ → (F ‘A) = (G ‘A))

Proof of Theorem fveq1d

Step	Hyp	Ref	Expression
1		fveq1d.1	. 2 ⊢ (φ → F = G)
2		fveq1 5328	. 2 ⊢ (F = G → (F ‘A) = (G ‘A))
3	1, 2	syl 15	1 ⊢ (φ → (F ‘A) = (G ‘A))

Syntax hints:   → wi 4   = 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:  fveq12d  5334  csbfv2g  5338  funssfv  5344  fvunsn  5445  fvsng  5447  f1ocnvfv1  5477  fvmptd  5703