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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 | |
eqssi.2 |
Ref | Expression |
---|---|
eqssi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqssi.1 | . 2 | |
2 | eqssi.2 | . 2 | |
3 | eqss 3152 | . 2 | |
4 | 1, 2, 3 | mpbir2an 931 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wss 3111 |
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-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-in 3117 df-ss 3124 |
This theorem is referenced by: inv1 3440 unv 3441 undifabs 3480 intab 3847 intid 4196 find 4570 limom 4585 dmv 4814 0ima 4958 rnxpid 5032 dftpos4 6222 axaddf 7800 axmulf 7801 dfuzi 9292 unirnioo 9900 txuni2 12803 dvef 13235 reeff1o 13241 |
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