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Theorem 19.36iv 1938
Description: Inference associated with 19.36v 1985. Version of 19.36i 2223 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 1961. (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 1937 . 2 (∃𝑥(𝜑𝜓) → (∀𝑥𝜑𝜓))
31, 2ax-mp 5 1 (∀𝑥𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  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
This theorem depends on definitions:  df-bi 208  df-ex 1772
This theorem is referenced by:  spimvALT  2400  vtocl  3557  vtocl2OLD  3560  zfcndext  10023
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