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Theorem 19.29r 1876
 Description: Variation of 19.29 1875. (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 pm3.21 475 . . 3 (𝜓 → (𝜑 → (𝜑𝜓)))
21aleximi 1833 . 2 (∀𝑥𝜓 → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
32impcom 411 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:  19.29r2  1877  19.29x  1878  intab  4879  imadif  6411  kmlem6  9558  hashgt23el  13769  2ndcdisj  22039  fmcncfil  31181  bnj907  32246  funen1cnv  32364  loop1cycl  32391  umgr2cycl  32395  bj-19.41al  33999
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