MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.01da Structured version   Visualization version   Unicode version

Theorem pm2.01da 449
Description: Deduction based on reductio ad absurdum. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
pm2.01da.1  |-  ( (
ph  /\  ps )  ->  -.  ps )
Assertion
Ref Expression
pm2.01da  |-  ( ph  ->  -.  ps )

Proof of Theorem pm2.01da
StepHypRef Expression
1 pm2.01da.1 . . 3  |-  ( (
ph  /\  ps )  ->  -.  ps )
21ex 441 . 2  |-  ( ph  ->  ( ps  ->  -.  ps ) )
32pm2.01d 174 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 376
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 190  df-an 378
This theorem is referenced by:  efrirr  4820  omlimcl  7297  hartogslem1  8075  cfslb2n  8716  fin23lem41  8800  tskuni  9226  4sqlem18OLD  14985  4sqlem18  14991  ramlb  15056  ivthlem2  22481  ivthlem3  22482  cosne0  23558  footne  24844
  Copyright terms: Public domain W3C validator