Theorem oveqi 5626

Description: Equality inference for operation value. (Contributed by NM, 24-Nov-2007.)

Hypothesis

Ref	Expression
oveq1i.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
oveqi	⊢ (𝐶𝐴𝐷) = (𝐶𝐵𝐷)

Proof of Theorem oveqi

Step	Hyp	Ref	Expression
1		oveq1i.1	. 2 ⊢ 𝐴 = 𝐵
2		oveq 5619	. 2 ⊢ (𝐴 = 𝐵 → (𝐶𝐴𝐷) = (𝐶𝐵𝐷))
3	1, 2	ax-mp 7	1 ⊢ (𝐶𝐴𝐷) = (𝐶𝐵𝐷)

Syntax hints:   = wceq 1287  (class class class)co 5613

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067

This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rex 2361  df-uni 3637  df-br 3821  df-iota 4946  df-fv 4989  df-ov 5616

This theorem is referenced by:  oveq123i  5627  iseqvalcbv  9789