Theorem 19.23bi 2203

Description: Inference form of Theorem 19.23 of [Margaris] p. 90, see 19.23 2223. (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 2193	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
2		19.23bi.1	. 2 ⊢ (∃𝑥𝜑 → 𝜓)
3	1, 2	syl 17	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-12 2189

This theorem depends on definitions:  df-bi 208  df-ex 1787

This theorem is referenced by:  nf5ri  2207  equs5eALT  2375  equs5e  2466  2mo  2652  copsexg  5432  axreg2  9498  hash1to3  14445  ustuqtop4  24227  f1omptsnlem  37698  mptsnunlem  37700