Theorem 19.23bi 2227

Description: Inference form of Theorem 19.23 of [Margaris] p. 90, see 19.23 2247. (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 2217	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
2		19.23bi.1	. 2 ⊢ (∃𝑥𝜑 → 𝜓)
3	1, 2	syl 18	1 ⊢ (𝜑 → 𝜓)

This proof depends on syntax axioms:   → wi 4  ∃wex 1811

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-12 2212

This proof depends on definitions:  df-bi 210  df-ex 1812

This theorem is used by:  nf5ri  2231  equs5eALT  2396  equs5e  2487  2mo  2673  copsexg  5462  axreg2  9594  hash1to3  14644  ustuqtop4  24572  f1omptsnlem  38368  mptsnunlem  38370