Theorem bj-sylget 37254

Description: Dual statement of sylgt 1851. Closed form of bj-sylge 37257. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-sylget	⊢ (∀𝑥(𝜒 → 𝜑) → ((∃𝑥𝜑 → 𝜓) → (∃𝑥𝜒 → 𝜓)))

Proof of Theorem bj-sylget

Step	Hyp	Ref	Expression
1		exim 1863	. 2 ⊢ (∀𝑥(𝜒 → 𝜑) → (∃𝑥𝜒 → ∃𝑥𝜑))
2	1	imim1d 83	1 ⊢ (∀𝑥(𝜒 → 𝜑) → ((∃𝑥𝜑 → 𝜓) → (∃𝑥𝜒 → 𝜓)))

This proof depends on syntax axioms:   → wi 4  ∀wal 1567  ∃wex 1808

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838

This proof depends on definitions:  df-bi 210  df-ex 1809

This theorem is used by:  bj-sylget2  37255  bj-exlimg  37256