Theorem bj-sylget 37081

Description: Dual statement of sylgt 1844. Closed form of bj-sylge 37084. (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 1856	. 2 ⊢ (∀𝑥(𝜒 → 𝜑) → (∃𝑥𝜒 → ∃𝑥𝜑))
2	1	imim1d 82	1 ⊢ (∀𝑥(𝜒 → 𝜑) → ((∃𝑥𝜑 → 𝜓) → (∃𝑥𝜒 → 𝜓)))

Syntax hints:   → wi 4  ∀wal 1560  ∃wex 1801

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831

This theorem depends on definitions:  df-bi 209  df-ex 1802

This theorem is referenced by:  bj-sylget2  37082  bj-exlimg  37083