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

Metamath Proof Explorer

Theorem spesbcd

Description: form of spsbc . (Contributed by Mario Carneiro, 9-Feb-2017)

		Ref	Expression
	Hypothesis	spesbcd.1	$⊢ φ \to \underset{˙}{[} A / x \underset{˙}{]} ψ$
	Assertion	spesbcd	$⊢ φ \to \exists x ψ$

Step	Hyp	Ref	Expression
1		spesbcd.1	$⊢ φ \to \underset{˙}{[} A / x \underset{˙}{]} ψ$
2		spesbc	$⊢ \underset{˙}{[} A / x \underset{˙}{]} ψ \to \exists x ψ$
3	1 2	syl	$⊢ φ \to \exists x ψ$