Theorem bj-sylge 36626

Description: Dual statement of sylg 1822 (the final "e" in the label stands for "existential (version of sylg 1822)". Variant of exlimih 2288. (Contributed by BJ, 25-Dec-2023.)

Hypotheses

Ref	Expression
bj-sylge.nf	⊢ (∃𝑥𝜑 → 𝜓)
bj-sylge.maj	⊢ (𝜒 → 𝜑)

Assertion

Ref	Expression
bj-sylge	⊢ (∃𝑥𝜒 → 𝜓)

Proof of Theorem bj-sylge

Step	Hyp	Ref	Expression
1		bj-sylge.maj	. . 3 ⊢ (𝜒 → 𝜑)
2	1	eximi 1834	. 2 ⊢ (∃𝑥𝜒 → ∃𝑥𝜑)
3		bj-sylge.nf	. 2 ⊢ (∃𝑥𝜑 → 𝜓)
4	2, 3	syl 17	1 ⊢ (∃𝑥𝜒 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1778

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808

This theorem depends on definitions:  df-bi 207  df-ex 1779

This theorem is referenced by:  bj-cbvexiw  36673