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Theorem 19.40 1973
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 1971 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
2 exsimpr 1972 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
31, 2jca 509 1 (∃𝑥(𝜑𝜓) → (∃𝑥𝜑 ∧ ∃𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 386  wex 1880
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910
This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1881
This theorem is referenced by:  19.40-2  1991  19.40b  1992  19.41v  2050  19.41vOLD  2102  19.41  2280  exdistrf  2469  uniin  4681  copsexg  5177  dmin  5565  imadif  6207  bj-19.41al  33174
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