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Theorem 19.37aiv 1638
Description: Inference from Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.37aiv.1 𝑥(𝜑𝜓)
Assertion
Ref Expression
19.37aiv (𝜑 → ∃𝑥𝜓)
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem 19.37aiv
StepHypRef Expression
1 19.37aiv.1 . 2 𝑥(𝜑𝜓)
2 nfv 1493 . . 3 𝑥𝜑
3219.37-1 1637 . 2 (∃𝑥(𝜑𝜓) → (𝜑 → ∃𝑥𝜓))
41, 3ax-mp 5 1 (𝜑 → ∃𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-nf 1422
This theorem is referenced by:  eqvinc  2782  limom  4497
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