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Theorem 19.29r 1954
Description: Variation of 19.29 1953. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Nov-2020.)
Assertion
Ref Expression
19.29r ((∃𝑥𝜑 ∧ ∀𝑥𝜓) → ∃𝑥(𝜑𝜓))

Proof of Theorem 19.29r
StepHypRef Expression
1 pm3.21 448 . . 3 (𝜓 → (𝜑 → (𝜑𝜓)))
21aleximi 1907 . 2 (∀𝑥𝜓 → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
32impcom 394 1 ((∃𝑥𝜑 ∧ ∀𝑥𝜓) → ∃𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wal 1629  wex 1852
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853
This theorem is referenced by:  19.29r2  1955  19.29x  1956  intab  4641  imadif  6113  kmlem6  9179  2ndcdisj  21480  fmcncfil  30317  bnj907  31373  bj-19.41al  32974
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