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Theorem 19.36iv 2025
Description: Inference associated with 19.36v 2071. Version of 19.36i 2254 with a dv condition. (Contributed by NM, 5-Aug-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 17-Jan-2020.) Remove dependency on ax-6 2056. (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 2024 . 2 (∃𝑥(𝜑𝜓) → (∀𝑥𝜑𝜓))
31, 2ax-mp 5 1 (∀𝑥𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1628  wex 1851
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990
This theorem depends on definitions:  df-bi 197  df-ex 1852
This theorem is referenced by:  spimvALT  2419  vtocl  3408  vtocl2  3410  vtocl3  3411  zfcndext  9636  bj-spimvv  33052
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