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Theorem 19.29 1789
 Description: Theorem 19.29 of [Margaris] p. 90. See also 19.29r 1790. (Contributed by NM, 21-Jun-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
19.29 ((∀𝑥𝜑 ∧ ∃𝑥𝜓) → ∃𝑥(𝜑𝜓))

Proof of Theorem 19.29
StepHypRef Expression
1 pm3.2 462 . . 3 (𝜑 → (𝜓 → (𝜑𝜓)))
21aleximi 1749 . 2 (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥(𝜑𝜓)))
32imp 444 1 ((∀𝑥𝜑 ∧ ∃𝑥𝜓) → ∃𝑥(𝜑𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383  ∀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 This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696 This theorem is referenced by:  19.29rOLD  1791  19.29x  1793  19.40bOLD  1805  supsrlem  9811  1stccnp  21075  iscmet3  22899  isch3  27482  bnj849  30249  axc11n11r  31860  stoweidlem35  38928
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