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Theorem 19.23OLD 2217
 Description: Obsolete proof of 19.23 2078 as of 6-Oct-2021. (Contributed by NM, 24-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
19.23OLD.1 𝑥𝜓
Assertion
Ref Expression
19.23OLD (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))

Proof of Theorem 19.23OLD
StepHypRef Expression
1 19.23OLD.1 . 2 𝑥𝜓
2 19.23tOLD 2216 . 2 (Ⅎ𝑥𝜓 → (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓)))
31, 2ax-mp 5 1 (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196  ∀wal 1479  ∃wex 1702  ℲwnfOLD 1707 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:  19.23hOLD  2218  exlimiOLD  2219
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