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 → 𝐴 = 𝐵 )
Assertion	uneq1d	⊢ ( 𝜑 → ( 𝐴 ∪ 𝐶 ) = ( 𝐵 ∪ 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		uneq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		uneq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∪ 𝐶 ) = ( 𝐵 ∪ 𝐶 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 ∪ 𝐶 ) = ( 𝐵 ∪ 𝐶 ) )