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Theorem 19.40 1880
 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 1862 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
2 exsimpr 1863 . 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 1773 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803 This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1774 This theorem is referenced by:  19.40-2  1881  19.40b  1882  19.41v  1943  19.41  2230  exdistrf  2466  uniin  4857  copsexgw  5378  copsexg  5379  dmin  5779  imadif  6435  oprabidw  7179  lfuhgr3  32250  bj-19.41al  33876  bj-nnfan  33961  bj-nnfand  33962  bj-19.42t  33986
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