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Theorem dtrucor 4224
Description: Corollary of dtru 4217. 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 4225. (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 4217 . . 3  |-  -.  A. x  x  =  y
21pm2.21i 123 . 2  |-  ( A. x  x  =  y  ->  x  =/=  y )
3 dtrucor.1 . 2  |-  x  =  y
42, 3mpg 1538 1  |-  x  =/=  y
Colors of variables: wff set class
Syntax hints:   A.wal 1530    = wceq 1632    =/= wne 2459
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-nul 4165  ax-pow 4204
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535
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