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Theorem 19.36ivOLD 2062
 Description: Obsolete version of 19.36iv 2015 as of 15-Apr-2022. (Contributed by NM, 5-Aug-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 17-Jan-2020.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
19.36ivOLD.1 𝑥(𝜑𝜓)
Assertion
Ref Expression
19.36ivOLD (∀𝑥𝜑𝜓)
Distinct variable group:   𝜓,𝑥
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem 19.36ivOLD
StepHypRef Expression
1 19.36ivOLD.1 . 2 𝑥(𝜑𝜓)
2 19.36v 2061 . 2 (∃𝑥(𝜑𝜓) ↔ (∀𝑥𝜑𝜓))
31, 2mpbi 220 1 (∀𝑥𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1622  ∃wex 1845 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1863  ax-4 1878  ax-5 1980  ax-6 2046 This theorem depends on definitions:  df-bi 197  df-ex 1846 This theorem is referenced by: (None)
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