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Theorem 19.23h 2287
Description: Theorem 19.23 of [Margaris] p. 90. See 19.23 2201. (Contributed by NM, 24-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 1-Jan-2018.)
Hypothesis
Ref Expression
19.23h.1 (𝜓 → ∀𝑥𝜓)
Assertion
Ref Expression
19.23h (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))

Proof of Theorem 19.23h
StepHypRef Expression
1 19.23h.1 . . 3 (𝜓 → ∀𝑥𝜓)
21nf5i 2141 . 2 𝑥𝜓
3219.23 2201 1 (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wal 1526  wex 1771
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-10 2136  ax-12 2167
This theorem depends on definitions:  df-bi 208  df-ex 1772  df-nf 1776
This theorem is referenced by: (None)
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