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Theorem dtrucor2 4209
Description: The theorem form of the deduction dtrucor 4208 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 a9e 1891 . 2  |-  E. x  x  =  y
2 dtrucor2.1 . . . . 5  |-  ( x  =  y  ->  x  =/=  y )
32necon2bi 2492 . . . 4  |-  ( x  =  y  ->  -.  x  =  y )
4 pm2.01 160 . . . 4  |-  ( ( x  =  y  ->  -.  x  =  y
)  ->  -.  x  =  y )
53, 4ax-mp 8 . . 3  |-  -.  x  =  y
65nex 1542 . 2  |-  -.  E. x  x  =  y
71, 6pm2.24ii 124 1  |-  ( ph  /\ 
-.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358   E.wex 1528    = wceq 1623    =/= wne 2446
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-ne 2448
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