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Theorem oveqd 5539
Description: Equality deduction for operation value. (Contributed by set.mm contributors, 9-Sep-2006.)
Hypothesis
Ref Expression
oveq1d.1 (φA = B)
Assertion
Ref Expression
oveqd (φ → (CAD) = (CBD))

Proof of Theorem oveqd
StepHypRef Expression
1 oveq1d.1 . 2 (φA = B)
2 oveq 5529 . 2 (A = B → (CAD) = (CBD))
31, 2syl 15 1 (φ → (CAD) = (CBD))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1642  (class class class)co 5525
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 2478  df-rex 2620  df-uni 3892  df-iota 4339  df-br 4640  df-fv 4795  df-ov 5526
This theorem is referenced by:  oveq123d  5543  csbov12g  5553  oprssov  5603
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