MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.24ii Structured version   Visualization version   Unicode version

Theorem pm2.24ii 137
Description: A contradiction implies anything. Inference associated with pm2.21i 136 and pm2.24i 138. (Contributed by NM, 27-Feb-2008.)
Hypotheses
Ref Expression
pm2.24ii.1  |-  ph
pm2.24ii.2  |-  -.  ph
Assertion
Ref Expression
pm2.24ii  |-  ps

Proof of Theorem pm2.24ii
StepHypRef Expression
1 pm2.24ii.1 . 2  |-  ph
2 pm2.24ii.2 . . 3  |-  -.  ph
32pm2.21i 136 . 2  |-  ( ph  ->  ps )
41, 3ax-mp 5 1  |-  ps
Colors of variables: wff setvar class
Syntax hints:   -. wn 3
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  dtrucor2  4647  bj-babygodel  31231  bj-dtrucor2v  31460
  Copyright terms: Public domain W3C validator