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Theorem bj-dvdemo1 31796
Description: Remove dependency on ax-13 2233 from dvdemo1 4824 (this removal is noteworthy since dvdemo1 4824 and dvdemo2 4825 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 31791 . . 3 ¬ ∀𝑥 𝑥 = 𝑦
2 exnal 1743 . . 3 (∃𝑥 ¬ 𝑥 = 𝑦 ↔ ¬ ∀𝑥 𝑥 = 𝑦)
31, 2mpbir 219 . 2 𝑥 ¬ 𝑥 = 𝑦
4 pm2.21 118 . 2 𝑥 = 𝑦 → (𝑥 = 𝑦𝑧𝑥))
53, 4eximii 1753 1 𝑥(𝑥 = 𝑦𝑧𝑥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1472  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-8 1978  ax-9 1985  ax-10 2005  ax-11 2020  ax-12 2033  ax-nul 4712  ax-pow 4764
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700
This theorem is referenced by: (None)
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