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Theorem zfcndext 10653
Description: Axiom of Extensionality ax-ext 2708, reproved from conditionless ZFC version and predicate calculus. Usage of this theorem is discouraged because it depends on ax-13 2377. (Contributed by NM, 15-Aug-2003.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
zfcndext (∀𝑧(𝑧𝑥𝑧𝑦) → 𝑥 = 𝑦)
Distinct variable group:   𝑥,𝑦,𝑧

Proof of Theorem zfcndext
StepHypRef Expression
1 axextnd 10631 . 2 𝑧((𝑧𝑥𝑧𝑦) → 𝑥 = 𝑦)
2119.36iv 1946 1 (∀𝑧(𝑧𝑥𝑧𝑦) → 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  wal 1538   = wceq 1540  wcel 2108
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-13 2377  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-nf 1784  df-clel 2816  df-nfc 2892
This theorem is referenced by: (None)
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