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

Step	Hyp	Ref	Expression
1		fveq1 5327	. 2 |- (F = G -> (F` <.A, B>.) = (G` <.A, B>.))
2		df-ov 5526	. 2 |- (AFB) = (F` <.A, B>.)
3		df-ov 5526	. 2 |- (AGB) = (G` <.A, B>.)
4	1, 2, 3	3eqtr4g 2410	1 |- (F = G -> (AFB) = (AGB))

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