Theorem oveqd 5540

Description: Equality deduction for operation value. (Contributed by set.mm contributors, 9-Sep-2006.)

Hypothesis

Ref	Expression
oveq1d.1	⊢ (φ → A = B)

Assertion

Ref	Expression
oveqd	⊢ (φ → (CAD) = (CBD))

Proof of Theorem oveqd

Step	Hyp	Ref	Expression
1		oveq1d.1	. 2 ⊢ (φ → A = B)
2		oveq 5530	. 2 ⊢ (A = B → (CAD) = (CBD))
3	1, 2	syl 15	1 ⊢ (φ → (CAD) = (CBD))

Syntax hints:   → wi 4   = wceq 1642  (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:  oveq123d  5544  csbov12g  5554  oprssov  5604