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Theorem 19.36iv 1902
Description: Inference associated with 19.36v 1901. Version of 19.36i 2097 with a dv condition. (Contributed by NM, 5-Aug-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 17-Jan-2020.)
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 19.36v 1901 . 2 (∃𝑥(𝜑𝜓) ↔ (∀𝑥𝜑𝜓))
31, 2mpbi 220 1 (∀𝑥𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  wex 1701
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885
This theorem depends on definitions:  df-bi 197  df-ex 1702
This theorem is referenced by:  spimv  2256  vtocl  3245  vtocl2  3247  vtocl3  3248  zfcndext  9379  bj-spimvv  32363
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