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Theorem zfcndext 9770
Description: Axiom of Extensionality ax-ext 2754, reproved from conditionless ZFC version and predicate calculus. (Contributed by NM, 15-Aug-2003.) (Proof modification is discouraged.)
Assertion
Ref Expression
zfcndext (∀𝑧(𝑧𝑥𝑧𝑦) → 𝑥 = 𝑦)
Distinct variable group:   𝑥,𝑦,𝑧

Proof of Theorem zfcndext
StepHypRef Expression
1 axextnd 9748 . 2 𝑧((𝑧𝑥𝑧𝑦) → 𝑥 = 𝑦)
2119.36iv 1989 1 (∀𝑧(𝑧𝑥𝑧𝑦) → 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198  wal 1599   = wceq 1601  wcel 2107
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-8 2109  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-13 2334  ax-ext 2754
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-tru 1605  df-ex 1824  df-nf 1828  df-nfc 2921
This theorem is referenced by: (None)
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