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Theorem dvdemo2 5032
Description: Demonstration of a theorem (scheme) that requires (meta)variables 𝑥 and 𝑧 to be distinct, but no others. It bundles the theorem schemes 𝑥(𝑥 = 𝑥𝑧𝑥) and 𝑥(𝑥 = 𝑦𝑦𝑥). Compare dvdemo1 5031. (Contributed by NM, 1-Dec-2006.)
Assertion
Ref Expression
dvdemo2 𝑥(𝑥 = 𝑦𝑧𝑥)
Distinct variable group:   𝑥,𝑧

Proof of Theorem dvdemo2
StepHypRef Expression
1 el 4979 . 2 𝑥 𝑧𝑥
2 ax-1 6 . 2 (𝑧𝑥 → (𝑥 = 𝑦𝑧𝑥))
31, 2eximii 1912 1 𝑥(𝑥 = 𝑦𝑧𝑥)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1852
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-8 2147  ax-9 2154  ax-12 2203  ax-13 2408  ax-pow 4975
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853  df-nf 1858
This theorem is referenced by: (None)
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