MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  mt2 Structured version   Unicode version

Theorem mt2 182
Description: A rule similar to modus tollens. Inference associated with con2i 123. (Contributed by NM, 19-Aug-1993.) (Proof shortened by Wolf Lammen, 10-Sep-2013.)
Hypotheses
Ref Expression
mt2.1  |-  ps
mt2.2  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
mt2  |-  -.  ph

Proof of Theorem mt2
StepHypRef Expression
1 mt2.1 . . 3  |-  ps
21a1i 11 . 2  |-  ( ph  ->  ps )
3 mt2.2 . 2  |-  ( ph  ->  -.  ps )
42, 3pm2.65i 176 1  |-  -.  ph
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  bijust  186  ax6dgen  1873  elirrv  8103  cardom  8410  0nnn  10630  nthruz  14271  hauspwdom  20453  fin1aufil  20884  rectbntr0  21787  lgam1  23893  gam1  23894  wlkntrl  25178  ex-po  25771  strlem1  27779  eulerpartlemt  29071  nalf  30889
  Copyright terms: Public domain W3C validator