MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.35 Unicode version

Theorem 19.35 1687
Description: Theorem 19.35 of [Margaris] p. 90. This theorem is useful for moving an implication (in the form of the right-hand side) into the scope of a single existential quantifier. (Contributed by NM, 12-Mar-1993.) (Proof shortened by Wolf Lammen, 27-Jun-2014.)
Assertion
Ref Expression
19.35

Proof of Theorem 19.35
StepHypRef Expression
1 pm2.27 39 . . . 4
21aleximi 1653 . . 3
32com12 31 . 2
4 exnal 1648 . . . 4
5 pm2.21 108 . . . . 5
65eximi 1656 . . . 4
74, 6sylbir 213 . . 3
8 exa1 1661 . . 3
97, 8ja 161 . 2
103, 9impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612
This theorem is referenced by:  19.35i  1689  19.35ri  1690  19.25  1691  19.43  1693  speimfwOLD  1736  19.39  1757  19.24  1758  19.36v  1762  19.37v  1768  19.36  1964  19.37  1966  spimt  2005  grothprim  9233  bj-nalnaleximiOLD  34222  bj-exaleximi  34224  bj-spimt2  34269  bj-spimtv  34278  bj-snsetex  34521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631
This theorem depends on definitions:  df-bi 185  df-ex 1613
  Copyright terms: Public domain W3C validator