MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.40 Structured version   Visualization version   GIF version

Theorem 19.40 1968
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 1966 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
2 exsimpr 1967 . 2 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
31, 2jca 508 1 (∃𝑥(𝜑𝜓) → (∃𝑥𝜑 ∧ ∃𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 385  wex 1875
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905
This theorem depends on definitions:  df-bi 199  df-an 386  df-ex 1876
This theorem is referenced by:  19.40-2  1986  19.40b  1987  19.41v  2045  19.41vOLD  2096  19.41  2270  exdistrf  2454  uniin  4649  copsexg  5145  dmin  5534  imadif  6183  bj-19.41al  33136
  Copyright terms: Public domain W3C validator