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Theorem 19.40 1878
Description: Theorem 19.40 of [Margaris] p. 90. (Contributed by NM, 26-May-1993.)
Assertion
Ref Expression
19.40 (∃𝑥(𝜑𝜓) → (∃𝑥𝜑 ∧ ∃𝑥𝜓))

Proof of Theorem 19.40
StepHypRef Expression
1 exsimpl 1860 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
2 exsimpr 1861 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
31, 2jca 512 1 (∃𝑥(𝜑𝜓) → (∃𝑥𝜑 ∧ ∃𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  wex 1771
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772
This theorem is referenced by:  19.40-2  1879  19.40b  1880  19.41v  1941  19.41  2227  exdistrf  2461  uniin  4850  copsexgw  5372  copsexg  5373  dmin  5773  imadif  6431  oprabidw  7176  lfuhgr3  32263  bj-19.41al  33889  bj-nnfan  33974  bj-nnfand  33975  bj-19.42t  33999
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