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Theorem bj-dvdemo1 33630
 Description: Remove dependency on ax-13 2301 from dvdemo1 5121 (this removal is noteworthy since dvdemo1 5121 and dvdemo2 5122 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 33625 . . 3 ¬ ∀𝑥 𝑥 = 𝑦
2 exnal 1789 . . 3 (∃𝑥 ¬ 𝑥 = 𝑦 ↔ ¬ ∀𝑥 𝑥 = 𝑦)
31, 2mpbir 223 . 2 𝑥 ¬ 𝑥 = 𝑦
4 pm2.21 121 . 2 𝑥 = 𝑦 → (𝑥 = 𝑦𝑧𝑥))
53, 4eximii 1799 1 𝑥(𝑥 = 𝑦𝑧𝑥)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1505  ∃wex 1742 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-12 2106  ax-nul 5061  ax-pow 5113 This theorem depends on definitions:  df-bi 199  df-an 388  df-ex 1743 This theorem is referenced by: (None)
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