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 ) )