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Theorem 19.39 1992
Description: Theorem 19.39 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
19.39 ((∃𝑥𝜑 → ∃𝑥𝜓) → ∃𝑥(𝜑𝜓))

Proof of Theorem 19.39
StepHypRef Expression
1 19.2 1982 . . 3 (∀𝑥𝜑 → ∃𝑥𝜑)
21imim1i 63 . 2 ((∃𝑥𝜑 → ∃𝑥𝜓) → (∀𝑥𝜑 → ∃𝑥𝜓))
3 19.35 1879 . 2 (∃𝑥(𝜑𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓))
42, 3sylibr 237 1 ((∃𝑥𝜑 → ∃𝑥𝜓) → ∃𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536  wex 1781
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-6 1971
This theorem depends on definitions:  df-bi 210  df-ex 1782
This theorem is referenced by: (None)
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