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Theorem 19.37iv 1949
 Description: Inference associated with 19.37v 1998. (Contributed by NM, 5-Aug-1993.) Remove dependency on ax-6 1970. (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 1948 . 2 (∃𝑥(𝜑𝜓) → (𝜑 → ∃𝑥𝜓))
31, 2ax-mp 5 1 (𝜑 → ∃𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃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:  bnd  9323  zfcndinf  10047  bnj1093  32428  bnj1186  32455  relopabVD  41778  elpglem2  45407
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