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Theorem 19.40 1889
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 1871 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
2 exsimpr 1872 . 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 1782
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783
This theorem is referenced by:  19.40-2  1890  19.40b  1891  19.41v  1953  19.41  2228  exdistrf  2447  uniin  4865  copsexgw  5404  copsexg  5405  dmin  5820  imadif  6518  oprabidw  7306  lfuhgr3  33081  bj-19.41al  34840  bj-nnfan  34930  bj-nnfand  34931  bj-19.42t  34955
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