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Theorem 19.36i 1605
Description: Inference from Theorem 19.36 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 2-Feb-2015.)
Hypotheses
Ref Expression
19.36i.1 𝑥𝜓
19.36i.2 𝑥(𝜑𝜓)
Assertion
Ref Expression
19.36i (∀𝑥𝜑𝜓)

Proof of Theorem 19.36i
StepHypRef Expression
1 19.36i.2 . . 3 𝑥(𝜑𝜓)
2119.35i 1559 . 2 (∀𝑥𝜑 → ∃𝑥𝜓)
3 19.36i.1 . . 3 𝑥𝜓
4 id 19 . . 3 (𝜓𝜓)
53, 4exlimi 1528 . 2 (∃𝑥𝜓𝜓)
62, 5syl 14 1 (∀𝑥𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1285  wnf 1392  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-ial 1470
This theorem depends on definitions:  df-bi 115  df-nf 1393
This theorem is referenced by:  19.36aiv  1826  vtoclf  2665
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