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Theorem 19.40 1783
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 1781 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
2 exsimpr 1782 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
31, 2jca 552 1 (∃𝑥(𝜑𝜓) → (∃𝑥𝜑 ∧ ∃𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695
This theorem is referenced by:  19.40-2  1801  19.40b  1802  19.40bOLD  1803  19.41v  1899  19.41  2087  exdistrf  2316  uniin  4383  copsexg  4872  dmin  5237  imadif  5869  bj-19.41al  31628
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