Metamath Proof Explorer


Theorem bnj1265

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

Ref Expression
Hypothesis bnj1265.1 ( 𝜑 → ∃ 𝑥𝐴 𝜓 )
Assertion bnj1265 ( 𝜑𝜓 )

Proof

Step Hyp Ref Expression
1 bnj1265.1 ( 𝜑 → ∃ 𝑥𝐴 𝜓 )
2 1 bnj1196 ( 𝜑 → ∃ 𝑥 ( 𝑥𝐴𝜓 ) )
3 2 bnj1266 ( 𝜑 → ∃ 𝑥 𝜓 )
4 3 bnj937 ( 𝜑𝜓 )