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Theorem 19.36iv 1947
 Description: Inference associated with 19.36v 1994. Version of 19.36i 2231 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 1970. (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 1946 . 2 (∃𝑥(𝜑𝜓) → (∀𝑥𝜑𝜓))
31, 2ax-mp 5 1 (∀𝑥𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1536  ∃wex 1781 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911 This theorem depends on definitions:  df-bi 210  df-ex 1782 This theorem is referenced by:  spimvALT  2398  vtocl2OLD  3510  zfcndext  10026
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