Theorem bj-sylgt2 37248

Description: Uncurried (imported) form of sylgt 1855. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-sylgt2	⊢ ((∀𝑥(𝜓 → 𝜒) ∧ (𝜑 → ∀𝑥𝜓)) → (𝜑 → ∀𝑥𝜒))

Proof of Theorem bj-sylgt2

Step	Hyp	Ref	Expression
1		sylgt 1855	. 2 ⊢ (∀𝑥(𝜓 → 𝜒) → ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜒)))
2	1	imp 412	1 ⊢ ((∀𝑥(𝜓 → 𝜒) ∧ (𝜑 → ∀𝑥𝜓)) → (𝜑 → ∀𝑥𝜒))

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

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

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

This theorem is used by: (None)