Theorem zfcndext 9435

Description: Axiom of Extensionality ax-ext 2602, reproved from conditionless ZFC version and predicate calculus. (Contributed by NM, 15-Aug-2003.) (Proof modification is discouraged.)

Assertion

Ref	Expression
zfcndext	|- ( A. z ( z e. x <-> z e. y ) -> x = y )

Distinct variable group:   x, y, z

Proof of Theorem zfcndext

Step	Hyp	Ref	Expression
1		axextnd 9413	. 2 |- E. z ( ( z e. x <-> z e. y ) -> x = y )
2	1	19.36iv 1905	1 |- ( A. z ( z e. x <-> z e. y ) -> x = y )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   = wceq 1483   e. wcel 1990

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-8 1992  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-cleq 2615  df-clel 2618  df-nfc 2753

This theorem is referenced by: (None)