Theorem bj-spnfw 37321

Description: Theorem close to a closed form of spnfw 2008. (Contributed by BJ, 12-May-2019.)

Assertion

Ref	Expression
bj-spnfw	⊢ ((∃𝑥𝜑 → 𝜓) → (∀𝑥𝜑 → 𝜓))

Proof of Theorem bj-spnfw

Step	Hyp	Ref	Expression
1		19.2 2005	. 2 ⊢ (∀𝑥𝜑 → ∃𝑥𝜑)
2	1	imim1i 64	1 ⊢ ((∃𝑥𝜑 → 𝜓) → (∀𝑥𝜑 → 𝜓))

This proof depends on syntax axioms:   → wi 4  ∀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  ax-6 1996

This proof depends on definitions:  df-bi 210  df-ex 1809

This theorem is used by: (None)