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Mirrors > Home > ILE Home > Th. List > sb10f | Unicode version |
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.) |
Ref | Expression |
---|---|
sb10f.1 |
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Ref | Expression |
---|---|
sb10f |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb10f.1 |
. . . 4
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2 | 1 | hbsb 1961 |
. . 3
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3 | sbequ 1851 |
. . 3
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4 | 2, 3 | equsex 1739 |
. 2
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5 | 4 | bicomi 132 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 |
This theorem is referenced by: (None) |
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