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Theorem 19.29 1877
Description: Theorem 19.29 of [Margaris] p. 90. See also 19.29r 1878. (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 pm3.2 471 . . 3 (𝜑 → (𝜓 → (𝜑𝜓)))
21aleximi 1835 . 2 (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥(𝜑𝜓)))
32imp 408 1 ((∀𝑥𝜑 ∧ ∃𝑥𝜓) → ∃𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  wal 1540  wex 1782
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783
This theorem is referenced by:  19.29x  1880  supsrlem  11054  1stccnp  22829  iscmet3  24673  isch3  30225  bnj849  33577  lfuhgr3  33753  axc11n11r  35177  bj-19.42t  35267  stoweidlem35  44350
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