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Theorem 19.37aiv 1608
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 1464 . . 3 𝑥𝜑
3219.37-1 1607 . 2 (∃𝑥(𝜑𝜓) → (𝜑 → ∃𝑥𝜓))
41, 3ax-mp 7 1 (𝜑 → ∃𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1424
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-17 1462  ax-ial 1470
This theorem depends on definitions:  df-bi 115  df-nf 1393
This theorem is referenced by:  eqvinc  2731  limom  4403
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