Theorem bj-sylget 34729

Description: Dual statement of sylgt 1825. Closed form of bj-sylge 34732. (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 1837	. 2 ⊢ (∀𝑥(𝜒 → 𝜑) → (∃𝑥𝜒 → ∃𝑥𝜑))
2	1	imim1d 82	1 ⊢ (∀𝑥(𝜒 → 𝜑) → ((∃𝑥𝜑 → 𝜓) → (∃𝑥𝜒 → 𝜓)))

Syntax hints:   → wi 4  ∀wal 1537  ∃wex 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813

This theorem depends on definitions:  df-bi 206  df-ex 1784

This theorem is referenced by:  bj-sylget2  34730  bj-exlimg  34731