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Theorem dtrucor 5259
Description: Corollary of dtru 5258. 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 5260. (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 5258 . . 3 ¬ ∀𝑥 𝑥 = 𝑦
21pm2.21i 119 . 2 (∀𝑥 𝑥 = 𝑦𝑥𝑦)
3 dtrucor.1 . 2 𝑥 = 𝑦
42, 3mpg 1799 1 𝑥𝑦
Colors of variables: wff setvar class
Syntax hints:  wal 1536  wne 3014
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-12 2179  ax-nul 5196  ax-pow 5253
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-nf 1786
This theorem is referenced by: (None)
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