Metamath Proof Explorer


Theorem xpeq1d

Description: Equality deduction for Cartesian product. (Contributed by Jeff Madsen, 17-Jun-2010)

Ref Expression
Hypothesis xpeq1d.1 φ A = B
Assertion xpeq1d φ A × C = B × C

Proof

Step Hyp Ref Expression
1 xpeq1d.1 φ A = B
2 xpeq1 A = B A × C = B × C
3 1 2 syl φ A × C = B × C