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Metamath Proof Explorer

Theorem uneq1d

Description: Deduction adding union to the right in a class equality. (Contributed by NM, 29-Mar-1998)

		Ref	Expression
	Hypothesis	uneq1d.1	$⊢ φ \to A = B$
	Assertion	uneq1d	$⊢ φ \to A \cup C = B \cup C$

Step	Hyp	Ref	Expression
1		uneq1d.1	$⊢ φ \to A = B$
2		uneq1	$⊢ A = B \to A \cup C = B \cup C$
3	1 2	syl	$⊢ φ \to A \cup C = B \cup C$