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Theorem 19.29 1875
 Description: Theorem 19.29 of [Margaris] p. 90. See also 19.29r 1876. (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 pm3.2 473 . . 3 (𝜑 → (𝜓 → (𝜑𝜓)))
21aleximi 1833 . 2 (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥(𝜑𝜓)))
32imp 410 1 ((∀𝑥𝜑 ∧ ∃𝑥𝜓) → ∃𝑥(𝜑𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399  ∀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 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782 This theorem is referenced by:  19.29x  1878  supsrlem  10520  1stccnp  22058  iscmet3  23888  isch3  29015  bnj849  32217  lfuhgr3  32386  axc11n11r  34037  bj-19.42t  34124  stoweidlem35  42534
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