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

Theorem 19.35ri 1695
Description: Inference associated with 19.35 1692. (Contributed by NM, 12-Mar-1993.)
Hypothesis
Ref Expression
19.35ri.1  |-  ( A. x ph  ->  E. x ps )
Assertion
Ref Expression
19.35ri  |-  E. x
( ph  ->  ps )

Proof of Theorem 19.35ri
StepHypRef Expression
1 19.35ri.1 . 2  |-  ( A. x ph  ->  E. x ps )
2 19.35 1692 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
31, 2mpbir 209 1  |-  E. x
( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1396   E.wex 1617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636
This theorem depends on definitions:  df-bi 185  df-ex 1618
This theorem is referenced by:  qexmid  1982  axrep1  4551  axextnd  8957  axinfnd  8973  bj-axrep1  34794
  Copyright terms: Public domain W3C validator