Theorem 19.23bi 1759

Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
19.23bi.1	⊢ (∃xφ → ψ)

Assertion

Ref	Expression
19.23bi	⊢ (φ → ψ)

Proof of Theorem 19.23bi

Step	Hyp	Ref	Expression
1		19.8a 1756	. 2 ⊢ (φ → ∃xφ)
2		19.23bi.1	. 2 ⊢ (∃xφ → ψ)
3	1, 2	syl 15	1 ⊢ (φ → ψ)

Syntax hints:   → wi 4  ∃wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  2mo  2282  nfunv  5139