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Theorem 19.40 1837
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 1835 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
2 exsimpr 1836 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
31, 2jca 553 1 (∃𝑥(𝜑𝜓) → (∃𝑥𝜑 ∧ ∃𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  wex 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745
This theorem is referenced by:  19.40-2  1854  19.40b  1855  19.41v  1917  19.41vOLD  1970  19.41  2141  exdistrf  2364  uniin  4489  copsexg  4985  dmin  5364  imadif  6011  bj-19.41al  32762
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