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Theorem 19.37iv 1908
Description: Inference associated with 19.37v 1907. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.37iv.1 𝑥(𝜑𝜓)
Assertion
Ref Expression
19.37iv (𝜑 → ∃𝑥𝜓)
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem 19.37iv
StepHypRef Expression
1 19.37iv.1 . 2 𝑥(𝜑𝜓)
2 19.37v 1907 . 2 (∃𝑥(𝜑𝜓) ↔ (𝜑 → ∃𝑥𝜓))
31, 2mpbi 220 1 (𝜑 → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  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:  eqvinc  3318  bnd  8715  zfcndinf  9400  bnj1093  30809  bnj1186  30836  relopabVD  38659  elpglem2  41778
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