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Theorem bj-dvdemo1 31990
 Description: Remove dependency on ax-13 2234 from dvdemo1 4829 (this removal is noteworthy since dvdemo1 4829 and dvdemo2 4830 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 31985 . . 3 ¬ ∀𝑥 𝑥 = 𝑦
2 exnal 1744 . . 3 (∃𝑥 ¬ 𝑥 = 𝑦 ↔ ¬ ∀𝑥 𝑥 = 𝑦)
31, 2mpbir 220 . 2 𝑥 ¬ 𝑥 = 𝑦
4 pm2.21 119 . 2 𝑥 = 𝑦 → (𝑥 = 𝑦𝑧𝑥))
53, 4eximii 1754 1 𝑥(𝑥 = 𝑦𝑧𝑥)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1473  ∃wex 1695 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-8 1979  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-nul 4717  ax-pow 4769 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701 This theorem is referenced by: (None)
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