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Mirrors > Home > ILE Home > Th. List > supeq1i | Unicode version |
Description: Equality inference for supremum. (Contributed by Paul Chapman, 22-Jun-2011.) |
Ref | Expression |
---|---|
supeq1i.1 |
Ref | Expression |
---|---|
supeq1i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | supeq1i.1 | . 2 | |
2 | supeq1 6942 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 csup 6938 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 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-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-rab 2451 df-uni 3784 df-sup 6940 |
This theorem is referenced by: infrenegsupex 9523 maxcom 11131 xrmax2sup 11181 xrmaxltsup 11185 xrmaxadd 11188 infxrnegsupex 11190 gcdcom 11891 gcdass 11933 |
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