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Theorem 19.40 1893
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 1875 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
2 exsimpr 1876 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
31, 2jca 515 1 (∃𝑥(𝜑𝜓) → (∃𝑥𝜑 ∧ ∃𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  wex 1786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1787
This theorem is referenced by:  19.40-2  1894  19.40b  1895  19.41v  1957  19.41  2237  exdistrf  2448  uniin  4832  copsexgw  5357  copsexg  5358  dmin  5764  imadif  6434  oprabidw  7214  lfuhgr3  32665  bj-19.41al  34496  bj-nnfan  34586  bj-nnfand  34587  bj-19.42t  34611
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