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Metamath Proof Explorer

Theorem bnj534

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

Ref Expression
Hypothesis bnj534.1 ⊢ ( 𝜒 → ( ∃ 𝑥 𝜑 ∧ 𝜓 ) )
Assertion bnj534 ( 𝜒 → ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 bnj534.1 ⊢ ( 𝜒 → ( ∃ 𝑥 𝜑 ∧ 𝜓 ) )
2 19.41v ⊢ ( ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) ↔ ( ∃ 𝑥 𝜑 ∧ 𝜓 ) )
3 1 2 sylibr ⊢ ( 𝜒 → ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) )