Theorem bj-sylget2 37337

Description: Uncurried (imported) form of bj-sylget 37336. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-sylget2	⊢ ((∀𝑥(𝜑 → 𝜓) ∧ (∃𝑥𝜓 → 𝜒)) → (∃𝑥𝜑 → 𝜒))

Proof of Theorem bj-sylget2

Step	Hyp	Ref	Expression
1		bj-sylget 37336	. 2 ⊢ (∀𝑥(𝜑 → 𝜓) → ((∃𝑥𝜓 → 𝜒) → (∃𝑥𝜑 → 𝜒)))
2	1	imp 412	1 ⊢ ((∀𝑥(𝜑 → 𝜓) ∧ (∃𝑥𝜓 → 𝜒)) → (∃𝑥𝜑 → 𝜒))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401  ∀wal 1568  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813

This theorem is used by: (None)