Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  exlimii Structured version   Visualization version   Unicode version

Theorem exlimii 31426
Description: Inference associated with exlimi 1994. Inferring a theorem when it is implied by an antecedent which may be true. (Contributed by BJ, 15-Sep-2018.)
Hypotheses
Ref Expression
exlimii.1  |-  F/ x ps
exlimii.2  |-  ( ph  ->  ps )
exlimii.3  |-  E. x ph
Assertion
Ref Expression
exlimii  |-  ps

Proof of Theorem exlimii
StepHypRef Expression
1 exlimii.3 . 2  |-  E. x ph
2 exlimii.1 . . 3  |-  F/ x ps
3 exlimii.2 . . 3  |-  ( ph  ->  ps )
42, 3exlimi 1994 . 2  |-  ( E. x ph  ->  ps )
51, 4ax-mp 5 1  |-  ps
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1662   F/wnf 1666
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-12 1932
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663  df-nf 1667
This theorem is referenced by:  exlimiieq1  31429  exlimiieq2  31430
  Copyright terms: Public domain W3C validator