Metamath Proof Explorer


Theorem equncom

Description: If a class equals the union of two other classes, then it equals the union of those two classes commuted. equncom was automatically derived from equncomVD using the tools program translate__without__overwriting.cmd and minimizing. (Contributed by Alan Sare, 18-Feb-2012)

Ref Expression
Assertion equncom ( 𝐴 = ( 𝐵𝐶 ) ↔ 𝐴 = ( 𝐶𝐵 ) )

Proof

Step Hyp Ref Expression
1 uncom ( 𝐵𝐶 ) = ( 𝐶𝐵 )
2 1 eqeq2i ( 𝐴 = ( 𝐵𝐶 ) ↔ 𝐴 = ( 𝐶𝐵 ) )