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Theorem dtrucor 4827
 Description: Corollary of dtru 4783. 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 4828. (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 4783 . . 3 ¬ ∀𝑥 𝑥 = 𝑦
21pm2.21i 115 . 2 (∀𝑥 𝑥 = 𝑦𝑥𝑦)
3 dtrucor.1 . 2 𝑥 = 𝑦
42, 3mpg 1715 1 𝑥𝑦
 Colors of variables: wff setvar class Syntax hints:  ∀wal 1473   ≠ wne 2780 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-8 1979  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-nul 4717  ax-pow 4769 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701 This theorem is referenced by: (None)
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