MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.8w Structured version   Unicode version

Theorem 19.8w 1800
Description: Weak version of 19.8a 1909. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 1-Aug-2017.) (Proof shortened by Wolf Lammen, 4-Dec-2017.)
Hypothesis
Ref Expression
19.8w.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
19.8w  |-  ( ph  ->  E. x ph )

Proof of Theorem 19.8w
StepHypRef Expression
1 19.8w.1 . 2  |-  ( ph  ->  A. x ph )
2 19.2 1799 . 2  |-  ( A. x ph  ->  E. x ph )
31, 2syl 17 1  |-  ( ph  ->  E. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1436   E.wex 1660
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-6 1795
This theorem depends on definitions:  df-bi 189  df-ex 1661
This theorem is referenced by:  19.8v  1801
  Copyright terms: Public domain W3C validator