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Theorem oveq 5529
 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
StepHypRef Expression
1 fveq1 5327 . 2 (F = G → (FA, B) = (GA, B))
2 df-ov 5526 . 2 (AFB) = (FA, B)
3 df-ov 5526 . 2 (AGB) = (GA, B)
41, 2, 33eqtr4g 2410 1 (F = G → (AFB) = (AGB))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  ⟨cop 4561   ‘cfv 4781  (class class class)co 5525 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 2478  df-rex 2620  df-uni 3892  df-iota 4339  df-br 4640  df-fv 4795  df-ov 5526 This theorem is referenced by:  oveqi  5536  oveqd  5539
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