Metamath Proof Explorer


Theorem bnj1322

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Assertion bnj1322 ( 𝐴 = 𝐵 → ( 𝐴𝐵 ) = 𝐴 )

Proof

Step Hyp Ref Expression
1 eqimss ( 𝐴 = 𝐵𝐴𝐵 )
2 df-ss ( 𝐴𝐵 ↔ ( 𝐴𝐵 ) = 𝐴 )
3 1 2 sylib ( 𝐴 = 𝐵 → ( 𝐴𝐵 ) = 𝐴 )