Metamath Proof Explorer


Theorem opeq2d

Description: Equality deduction for ordered pairs. (Contributed by NM, 16-Dec-2006)

Ref Expression
Hypothesis opeq1d.1 φ A = B
Assertion opeq2d φ C A = C B

Proof

Step Hyp Ref Expression
1 opeq1d.1 φ A = B
2 opeq2 A = B C A = C B
3 1 2 syl φ C A = C B