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

Theorem 19.35i 1733
Description: Inference associated with 19.35 1732. (Contributed by NM, 21-Jun-1993.)
Hypothesis
Ref Expression
19.35i.1  |-  E. x
( ph  ->  ps )
Assertion
Ref Expression
19.35i  |-  ( A. x ph  ->  E. x ps )

Proof of Theorem 19.35i
StepHypRef Expression
1 19.35i.1 . 2  |-  E. x
( ph  ->  ps )
2 19.35 1732 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
31, 2mpbi 211 1  |-  ( A. x ph  ->  E. x ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435   E.wex 1659
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678
This theorem depends on definitions:  df-bi 188  df-ex 1660
This theorem is referenced by:  19.2  1798  spimeh  1830  cbv3hv  2012  ax6e  2056  spimed  2061  equvini  2142  equveli  2143  euex  2290  axrep4  4537  zfcndrep  9040  bj-spimedv  31268  bj-axrep4  31364  wl-exeq  31781
  Copyright terms: Public domain W3C validator