Metamath Proof Explorer


Theorem opeq12d

Description: Equality deduction for ordered pairs. (Contributed by NM, 16-Dec-2006) (Proof shortened by Andrew Salmon, 29-Jun-2011)

Ref Expression
Hypotheses opeq1d.1 φ A = B
opeq12d.2 φ C = D
Assertion opeq12d φ A C = B D

Proof

Step Hyp Ref Expression
1 opeq1d.1 φ A = B
2 opeq12d.2 φ C = D
3 opeq12 A = B C = D A C = B D
4 1 2 3 syl2anc φ A C = B D