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Theorem dtrucor 4822
Description: Corollary of dtru 4778. 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 4823. (Contributed by NM, 27-Jun-2002.)
Hypothesis
Ref Expression
dtrucor.1 𝑥 = 𝑦
Assertion
Ref Expression
dtrucor 𝑥𝑦
Distinct variable group:   𝑥,𝑦

Proof of Theorem dtrucor
StepHypRef Expression
1 dtru 4778 . . 3 ¬ ∀𝑥 𝑥 = 𝑦
21pm2.21i 114 . 2 (∀𝑥 𝑥 = 𝑦𝑥𝑦)
3 dtrucor.1 . 2 𝑥 = 𝑦
42, 3mpg 1714 1 𝑥𝑦
Colors of variables: wff setvar class
Syntax hints:  wal 1472  wne 2779
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-8 1978  ax-9 1985  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-nul 4712  ax-pow 4764
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700
This theorem is referenced by: (None)
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