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Metamath Proof Explorer

Theorem xpeq1d

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

		Ref	Expression
	Hypothesis	xpeq1d.1	$⊢ φ \to A = B$
	Assertion	xpeq1d	$⊢ φ \to A \times C = B \times C$

Step	Hyp	Ref	Expression
1		xpeq1d.1	$⊢ φ \to A = B$
2		xpeq1	$⊢ A = B \to A \times C = B \times C$
3	1 2	syl	$⊢ φ \to A \times C = B \times C$