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Theorem 19.9d 1592
Description: A deduction version of one direction of 19.9 1576. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.9d.1 (𝜓 → Ⅎ𝑥𝜑)
Assertion
Ref Expression
19.9d (𝜓 → (∃𝑥𝜑𝜑))

Proof of Theorem 19.9d
StepHypRef Expression
1 19.9d.1 . . 3 (𝜓 → Ⅎ𝑥𝜑)
2 19.9t 1574 . . 3 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
31, 2syl 14 . 2 (𝜓 → (∃𝑥𝜑𝜑))
43biimpd 142 1 (𝜓 → (∃𝑥𝜑𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103  wnf 1390  wex 1422
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-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by: (None)
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