Metamath Proof Explorer


Theorem equncomi

Description: Inference form of equncom . equncomi was automatically derived from equncomiVD using the tools program translate__without__overwriting.cmd and minimizing. (Contributed by Alan Sare, 18-Feb-2012)

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

Proof

Step Hyp Ref Expression
1 equncomi.1 ⊢ 𝐴 = ( 𝐵 ∪ 𝐶 )
2 equncom ⊢ ( 𝐴 = ( 𝐵 ∪ 𝐶 ) ↔ 𝐴 = ( 𝐶 ∪ 𝐵 ) )
3 1 2 mpbi ⊢ 𝐴 = ( 𝐶 ∪ 𝐵 )