Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  sb10f Unicode version

Theorem sb10f 1968
 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.)
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
21hbsb 1920 . . 3
3 sbequ 1812 . . 3
42, 3equsex 1706 . 2
54bicomi 131 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1329  wex 1468  wsb 1735 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator