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Metamath Proof Explorer

Theorem bj-sylge

Description: Dual statement of sylg (the final "e" in the label stands for "existential (version of sylg )". Variant of exlimih . (Contributed by BJ, 25-Dec-2023)

	Ref	Expression
Hypotheses	bj-sylge.nf	$⊢ \exists x φ \to ψ$
	bj-sylge.maj	$⊢ χ \to φ$
Assertion	bj-sylge	$⊢ \exists x χ \to ψ$

Proof

Step	Hyp	Ref	Expression
1		bj-sylge.nf	$⊢ \exists x φ \to ψ$
2		bj-sylge.maj	$⊢ χ \to φ$
3	2	eximi	$⊢ \exists x χ \to \exists x φ$
4	3 1	syl	$⊢ \exists x χ \to ψ$