Theorem 19.23bi 2232

Description: Inference form of Theorem 19.23 of [Margaris] p. 90, see 19.23 2254. (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 2223	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
2		19.23bi.1	. 2 ⊢ (∃𝑥𝜑 → 𝜓)
3	1, 2	syl 17	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1878

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-12 2220

This theorem depends on definitions:  df-bi 199  df-ex 1879

This theorem is referenced by:  nf5ri  2236  equs5eALT  2387  equs5e  2479  dfmo  2668  2mo  2731  copsexg  5178  axreg2  8774  hash1to3  13569  ustuqtop4  22425  f1omptsnlem  33728  mptsnunlem  33730