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Theorem 19.29r 1790
 Description: Variation of 19.29 1789. (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 pm3.21 463 . . 3 (𝜓 → (𝜑 → (𝜑𝜓)))
21aleximi 1749 . 2 (∀𝑥𝜓 → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
32impcom 445 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:  19.29r2  1792  19.29x  1793  19.40bOLD  1805  intab  4442  imadif  5887  kmlem6  8860  2ndcdisj  21069  fmcncfil  29305  bnj907  30289  bj-19.41al  31826
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