Theorem oveq 5530

Description: Equality theorem for operation value. (Contributed by set.mm contributors, 28-Feb-1995.)

Assertion

Ref	Expression
oveq	⊢ (F = G → (AFB) = (AGB))

Proof of Theorem oveq

Step	Hyp	Ref	Expression
1		fveq1 5328	. 2 ⊢ (F = G → (F ‘⟨A, B⟩) = (G ‘⟨A, B⟩))
2		df-ov 5527	. 2 ⊢ (AFB) = (F ‘⟨A, B⟩)
3		df-ov 5527	. 2 ⊢ (AGB) = (G ‘⟨A, B⟩)
4	1, 2, 3	3eqtr4g 2410	1 ⊢ (F = G → (AFB) = (AGB))

Syntax hints:   → wi 4   = wceq 1642  ⟨cop 4562   ‘cfv 4782  (class class class)co 5526

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  df-ov 5527

This theorem is referenced by:  oveqi  5537  oveqd  5540