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Theorem 19.37iv 2047
Description: Inference associated with 19.37v 2096. (Contributed by NM, 5-Aug-1993.) Remove dependency on ax-6 2075. (Revised by Rohan Ridenour, 15-Apr-2022.)
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 19.37imv 2046 . 2 (∃𝑥(𝜑𝜓) → (𝜑 → ∃𝑥𝜓))
31, 2ax-mp 5 1 (𝜑 → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009
This theorem depends on definitions:  df-bi 199  df-ex 1879
This theorem is referenced by:  bnd  9032  zfcndinf  9755  bnj1093  31583  bnj1186  31610  relopabVD  39948  elpglem2  43346
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