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

Theorem jcai 536
Description: Deduction replacing implication with conjunction. (Contributed by NM, 15-Jul-1993.)
Hypotheses
Ref Expression
jcai.1  |-  ( ph  ->  ps )
jcai.2  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
jcai  |-  ( ph  ->  ( ps  /\  ch ) )

Proof of Theorem jcai
StepHypRef Expression
1 jcai.1 . 2  |-  ( ph  ->  ps )
2 jcai.2 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2mpd 15 . 2  |-  ( ph  ->  ch )
41, 3jca 532 1  |-  ( ph  ->  ( ps  /\  ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  reu6  3248  f1ocnv2d  6414  onfin2  7606  mpfrcl  17720  f1o3d  26092  oddpwdc  26874  altopthsn  28129  volsupnfl  28577  mbfresfi  28579  qirropth  29390  clwlkf1clwwlklem  30663  cpmatelimp  31178  cpmatelimp2  31180
  Copyright terms: Public domain W3C validator