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Theorem dtrucor 5072
 Description: Corollary of dtru 5071. 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 5073. (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 5071 . . 3 ¬ ∀𝑥 𝑥 = 𝑦
21pm2.21i 117 . 2 (∀𝑥 𝑥 = 𝑦𝑥𝑦)
3 dtrucor.1 . 2 𝑥 = 𝑦
42, 3mpg 1898 1 𝑥𝑦
 Colors of variables: wff setvar class Syntax hints:  ∀wal 1656   ≠ wne 3000 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-8 2168  ax-9 2175  ax-12 2222  ax-13 2391  ax-nul 5014  ax-pow 5066 This theorem depends on definitions:  df-bi 199  df-an 387  df-tru 1662  df-ex 1881  df-nf 1885 This theorem is referenced by: (None)
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