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Metamath Proof Explorer

Theorem 19.37imv

Description: One direction of 19.37v that can be proven without ax-6 . (Contributed by Rohan Ridenour, 16-Apr-2022)

Ref Expression
Assertion 19.37imv ⊢ ∃ x φ → ψ → φ → ∃ x ψ

Proof

Step Hyp Ref Expression
1 ax-5 ⊢ φ → ∀ x φ
2 19.35 ⊢ ∃ x φ → ψ ↔ ∀ x φ → ∃ x ψ
3 2 biimpi ⊢ ∃ x φ → ψ → ∀ x φ → ∃ x ψ
4 1 3 syl5 ⊢ ∃ x φ → ψ → φ → ∃ x ψ