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Theorem 19.34 1888
Description: Theorem 19.34 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
19.34 ((∀𝑥𝜑 ∨ ∃𝑥𝜓) → ∃𝑥(𝜑𝜓))

Proof of Theorem 19.34
StepHypRef Expression
1 19.2 1879 . . 3 (∀𝑥𝜑 → ∃𝑥𝜑)
21orim1i 538 . 2 ((∀𝑥𝜑 ∨ ∃𝑥𝜓) → (∃𝑥𝜑 ∨ ∃𝑥𝜓))
3 19.43 1799 . 2 (∃𝑥(𝜑𝜓) ↔ (∃𝑥𝜑 ∨ ∃𝑥𝜓))
42, 3sylibr 223 1 ((∀𝑥𝜑 ∨ ∃𝑥𝜓) → ∃𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 382  wal 1473  wex 1695
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-6 1875
This theorem depends on definitions:  df-bi 196  df-or 384  df-ex 1696
This theorem is referenced by: (None)
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