Theorem bj-sylget2 37255

Description: Uncurried (imported) form of bj-sylget 37254. (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 37254	. 2 ⊢ (∀𝑥(𝜑 → 𝜓) → ((∃𝑥𝜓 → 𝜒) → (∃𝑥𝜑 → 𝜒)))
2	1	imp 411	1 ⊢ ((∀𝑥(𝜑 → 𝜓) ∧ (∃𝑥𝜓 → 𝜒)) → (∃𝑥𝜑 → 𝜒))

This proof depends on syntax axioms:   → wi 4   ∧ wa 400  ∀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-an 401  df-ex 1809

This theorem is used by: (None)