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Theorem 19.25 1562
Description: Theorem 19.25 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 2-Feb-2015.)
Assertion
Ref Expression
19.25 (∀𝑦𝑥(𝜑𝜓) → (∃𝑦𝑥𝜑 → ∃𝑦𝑥𝜓))

Proof of Theorem 19.25
StepHypRef Expression
1 19.35-1 1560 . . 3 (∃𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∃𝑥𝜓))
21alimi 1389 . 2 (∀𝑦𝑥(𝜑𝜓) → ∀𝑦(∀𝑥𝜑 → ∃𝑥𝜓))
3 exim 1535 . 2 (∀𝑦(∀𝑥𝜑 → ∃𝑥𝜓) → (∃𝑦𝑥𝜑 → ∃𝑦𝑥𝜓))
42, 3syl 14 1 (∀𝑦𝑥(𝜑𝜓) → (∃𝑦𝑥𝜑 → ∃𝑦𝑥𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1287  wex 1426
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 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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