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Mirrors > Home > ILE Home > Th. List > eqssi | Unicode version |
Description: Infer equality from two subclass relationships. Compare Theorem 4 of [Suppes] p. 22. (Contributed by NM, 9-Sep-1993.) |
Ref | Expression |
---|---|
eqssi.1 |
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eqssi.2 |
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Ref | Expression |
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eqssi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqssi.1 |
. 2
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2 | eqssi.2 |
. 2
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3 | eqss 3170 |
. 2
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4 | 1, 2, 3 | mpbir2an 942 |
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-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-in 3135 df-ss 3142 |
This theorem is referenced by: inv1 3459 unv 3460 undifabs 3499 intab 3873 intid 4224 find 4598 limom 4613 dmv 4843 0ima 4988 rnxpid 5063 dftpos4 6263 axaddf 7866 axmulf 7867 dfuzi 9362 unirnioo 9972 txuni2 13692 dvef 14124 reeff1o 14130 |
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