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Theorem dtrucor 4633
Description: Corollary of dtru 4594. 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 4634. (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 4594 . . 3  |-  -.  A. x  x  =  y
21pm2.21i 135 . 2  |-  ( A. x  x  =  y  ->  x  =/=  y )
3 dtrucor.1 . 2  |-  x  =  y
42, 3mpg 1671 1  |-  x  =/=  y
Colors of variables: wff setvar class
Syntax hints:   A.wal 1442    =/= 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-8 1889  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-nul 4534  ax-pow 4581
This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668
This theorem is referenced by: (None)
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