Theorem 19.23bi 2228

Description: Inference form of Theorem 19.23 of [Margaris] p. 90, see 19.23 2248. (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 2218	. 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 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-12 2213

This proof depends on definitions:  df-bi 210  df-ex 1813

This theorem is used by:  nf5ri  2232  equs5eALT  2397  equs5e  2488  2mo  2674  copsexg  5462  axreg2  9580  hash1to3  14630  ustuqtop4  24556  f1omptsnlem  38239  mptsnunlem  38241