Theorem bj-spnfw 36630

Description: Theorem close to a closed form of spnfw 1978. (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 1975	. 2 ⊢ (∀𝑥𝜑 → ∃𝑥𝜑)
2	1	imim1i 63	1 ⊢ ((∃𝑥𝜑 → 𝜓) → (∀𝑥𝜑 → 𝜓))

Syntax hints:   → wi 4  ∀wal 1537  ∃wex 1778

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-6 1966

This theorem depends on definitions:  df-bi 207  df-ex 1779

This theorem is referenced by: (None)