Theorem 19.23bi 2199

Description: Inference form of Theorem 19.23 of [Margaris] p. 90, see 19.23 2219. (Contributed by NM, 12-Mar-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 2189	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
2		19.23bi.1	. 2 ⊢ (∃𝑥𝜑 → 𝜓)
3	1, 2	syl 17	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-12 2185

This theorem depends on definitions:  df-bi 207  df-ex 1782

This theorem is referenced by:  nf5ri  2203  equs5eALT  2372  equs5e  2463  2mo  2649  copsexg  5447  axreg2  9510  hash1to3  14427  ustuqtop4  24200  f1omptsnlem  37588  mptsnunlem  37590