This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem exbid

Description: Formula-building rule for existential quantifier (deduction form). (Contributed by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	albid.1	$⊢ Ⅎ x φ$
	albid.2	$⊢ φ \to (ψ \leftrightarrow χ)$
Assertion	exbid	$⊢ φ \to (\exists x ψ \leftrightarrow \exists x χ)$

Step	Hyp	Ref	Expression
1		albid.1	$⊢ Ⅎ x φ$
2		albid.2	$⊢ φ \to (ψ \leftrightarrow χ)$
3	1	nf5ri	$⊢ φ \to \forall x φ$
4	3 2	exbidh	$⊢ φ \to (\exists x ψ \leftrightarrow \exists x χ)$