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Theorem 19.40 1890
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 1872 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
2 exsimpr 1873 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
31, 2jca 513 1 (∃𝑥(𝜑𝜓) → (∃𝑥𝜑 ∧ ∃𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  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 398  df-ex 1783
This theorem is referenced by:  19.40-2  1891  19.40b  1892  19.41v  1954  19.41  2229  exdistrf  2447  uniin  4936  copsexgw  5491  copsexg  5492  dmin  5912  imadif  6633  oprabidw  7440  lfuhgr3  34110  bj-19.41al  35536  bj-nnfan  35626  bj-nnfand  35627  bj-19.42t  35651
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