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	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	exbidv	$$⊢\phi \to \left(\exists x\psi \leftrightarrow \exists x\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		albidv.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		ax-5	$$⊢\phi \to \forall x\phi$$
3	2 1	exbidh	$$⊢\phi \to \left(\exists x\psi \leftrightarrow \exists x\chi \right)$$