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Theorem dtrucor 4208
Description: Corollary of dtru 4201. This example illustrates the danger of blindly trusting the standard Deduction Theorem without accounting for free variables: the theorem form of this deduction is not valid, as shown by dtrucor2 4209. (Contributed by NM, 27-Jun-2002.)
Hypothesis
Ref Expression
dtrucor.1  |-  x  =  y
Assertion
Ref Expression
dtrucor  |-  x  =/=  y
Distinct variable group:    x, y

Proof of Theorem dtrucor
StepHypRef Expression
1 dtru 4201 . . 3  |-  -.  A. x  x  =  y
21pm2.21i 123 . 2  |-  ( A. x  x  =  y  ->  x  =/=  y )
3 dtrucor.1 . 2  |-  x  =  y
42, 3mpg 1535 1  |-  x  =/=  y
Colors of variables: wff set class
Syntax hints:   A.wal 1527    = 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-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-nul 4149  ax-pow 4188
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532
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