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Theorem 19.23hOLD 2218
 Description: Obsolete proof of 19.23h 2120 as of 6-Oct-2021. (Contributed by NM, 24-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 1-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
19.23hOLD.1 (𝜓 → ∀𝑥𝜓)
Assertion
Ref Expression
19.23hOLD (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))

Proof of Theorem 19.23hOLD
StepHypRef Expression
1 19.23hOLD.1 . . 3 (𝜓 → ∀𝑥𝜓)
21nfiOLD 1732 . 2 𝑥𝜓
3219.23OLD 2217 1 (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196  ∀wal 1479  ∃wex 1702 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-10 2017  ax-12 2045 This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1703  df-nf 1708  df-nfOLD 1719 This theorem is referenced by: (None)
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