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Metamath Proof Explorer

Theorem exbidv

Description: Formula-building rule for existential quantifier (deduction form). See also exbidh and exbid . (Contributed by NM, 26-May-1993)

Ref Expression
Hypothesis albidv.1 ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion exbidv ( 𝜑 → ( ∃ 𝑥 𝜓 ↔ ∃ 𝑥 𝜒 ) )

Proof

Step Hyp Ref Expression
1 albidv.1 ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2 ax-5 ⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
3 2 1 exbidh ⊢ ( 𝜑 → ( ∃ 𝑥 𝜓 ↔ ∃ 𝑥 𝜒 ) )