Metamath Proof Explorer


Theorem oveq12d

Description: Equality deduction for operation value. (Contributed by NM, 13-Mar-1995) (Proof shortened by Andrew Salmon, 22-Oct-2011)

Ref Expression
Hypotheses oveq1d.1 ⊢ φ → A = B
oveq12d.2 ⊢ φ → C = D
Assertion oveq12d ⊢ φ → A F C = B F D

Proof

Step Hyp Ref Expression
1 oveq1d.1 ⊢ φ → A = B
2 oveq12d.2 ⊢ φ → C = D
3 oveq12 ⊢ A = B ∧ C = D → A F C = B F D
4 1 2 3 syl2anc ⊢ φ → A F C = B F D