Metamath Proof Explorer


Theorem bnj228

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 9-Jul-2011) (New usage is discouraged.)

Ref Expression
Hypothesis bnj228.1 φxAψ
Assertion bnj228 xAφψ

Proof

Step Hyp Ref Expression
1 bnj228.1 φxAψ
2 rsp xAψxAψ
3 1 2 sylbi φxAψ
4 3 impcom xAφψ