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Metamath Proof Explorer

Theorem uneq1i

Description: Inference adding union to the right in a class equality. (Contributed by NM, 30-Aug-1993)

Ref Expression
Hypothesis uneq1i.1 ⊢ 𝐴 = 𝐵
Assertion uneq1i ( 𝐴 ∪ 𝐶 ) = ( 𝐵 ∪ 𝐶 )

Proof

Step Hyp Ref Expression
1 uneq1i.1 ⊢ 𝐴 = 𝐵
2 uneq1 ⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∪ 𝐶 ) = ( 𝐵 ∪ 𝐶 ) )
3 1 2 ax-mp ⊢ ( 𝐴 ∪ 𝐶 ) = ( 𝐵 ∪ 𝐶 )