MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  dtrucor2 Structured version   Visualization version   Unicode version

Theorem dtrucor2 4634
Description: The theorem form of the deduction dtrucor 4633 leads to a contradiction, as mentioned in the "Wrong!" example at http://us.metamath.org/mpeuni/mmdeduction.html#bad. (Contributed by NM, 20-Oct-2007.)
Hypothesis
Ref Expression
dtrucor2.1  |-  ( x  =  y  ->  x  =/=  y )
Assertion
Ref Expression
dtrucor2  |-  ( ph  /\ 
-.  ph )

Proof of Theorem dtrucor2
StepHypRef Expression
1 ax6e 2094 . 2  |-  E. x  x  =  y
2 dtrucor2.1 . . . . 5  |-  ( x  =  y  ->  x  =/=  y )
32necon2bi 2654 . . . 4  |-  ( x  =  y  ->  -.  x  =  y )
4 pm2.01 172 . . . 4  |-  ( ( x  =  y  ->  -.  x  =  y
)  ->  -.  x  =  y )
53, 4ax-mp 5 . . 3  |-  -.  x  =  y
65nex 1678 . 2  |-  -.  E. x  x  =  y
71, 6pm2.24ii 136 1  |-  ( ph  /\ 
-.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 371   E.wex 1663    =/= wne 2622
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-12 1933  ax-13 2091
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-ne 2624
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator