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Theorem 19.36iv 1942
Description: Inference associated with 19.36v 1983. Version of 19.36i 2219 with a disjoint variable condition. (Contributed by NM, 5-Aug-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 17-Jan-2020.) Remove dependency on ax-6 1963. (Revised by Rohan Ridenour, 15-Apr-2022.)
Hypothesis
Ref Expression
19.36iv.1 𝑥(𝜑𝜓)
Assertion
Ref Expression
19.36iv (∀𝑥𝜑𝜓)
Distinct variable group:   𝜓,𝑥
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem 19.36iv
StepHypRef Expression
1 19.36iv.1 . 2 𝑥(𝜑𝜓)
2 19.36imv 1940 . 2 (∃𝑥(𝜑𝜓) → (∀𝑥𝜑𝜓))
31, 2ax-mp 5 1 (∀𝑥𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1531  wex 1773
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905
This theorem depends on definitions:  df-bi 206  df-ex 1774
This theorem is referenced by:  spimvALT  2385  zfcndext  10644
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