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Theorem bj-dvdemo1 33138
Description: Remove dependency on ax-13 2408 from dvdemo1 5030 (this removal is noteworthy since dvdemo1 5030 and dvdemo2 5031 illustrate the phenomenon of bundling). (Contributed by BJ, 16-Jul-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-dvdemo1 𝑥(𝑥 = 𝑦𝑧𝑥)
Distinct variable group:   𝑥,𝑦

Proof of Theorem bj-dvdemo1
StepHypRef Expression
1 bj-dtru 33133 . . 3 ¬ ∀𝑥 𝑥 = 𝑦
2 exnal 1902 . . 3 (∃𝑥 ¬ 𝑥 = 𝑦 ↔ ¬ ∀𝑥 𝑥 = 𝑦)
31, 2mpbir 221 . 2 𝑥 ¬ 𝑥 = 𝑦
4 pm2.21 121 . 2 𝑥 = 𝑦 → (𝑥 = 𝑦𝑧𝑥))
53, 4eximii 1912 1 𝑥(𝑥 = 𝑦𝑧𝑥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1629  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-10 2174  ax-11 2190  ax-12 2203  ax-nul 4923  ax-pow 4974
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 835  df-tru 1634  df-ex 1853  df-nf 1858
This theorem is referenced by: (None)
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