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Theorem sb10f 2198
 Description: Hao Wang's identity axiom P6 in Irving Copi, Symbolic Logic (5th ed., 1979), p. 328. In traditional predicate calculus, this is a sole axiom for identity from which the usual ones can be derived. (Contributed by NM, 9-May-2005.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypothesis
Ref Expression
sb10f.1
Assertion
Ref Expression
sb10f
Distinct variable group:   ,
Allowed substitution hints:   (,,)

Proof of Theorem sb10f
StepHypRef Expression
1 sb10f.1 . . . 4
21nfsb 2184 . . 3
3 sbequ 2138 . . 3
42, 3equsex 2002 . 2
54bicomi 194 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550  wnf 1553  wsb 1658 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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