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Mirrors > Home > ILE Home > Th. List > ssbri | Unicode version |
Description: Inference from a subclass relationship of binary relations. (Contributed by NM, 28-Mar-2007.) (Revised by Mario Carneiro, 8-Feb-2015.) |
Ref | Expression |
---|---|
ssbri.1 |
Ref | Expression |
---|---|
ssbri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssbri.1 | . . . 4 | |
2 | 1 | a1i 9 | . . 3 |
3 | 2 | ssbrd 4008 | . 2 |
4 | 3 | mptru 1344 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wtru 1336 wss 3102 class class class wbr 3966 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-in 3108 df-ss 3115 df-br 3967 |
This theorem is referenced by: brel 4639 swoer 6509 swoord1 6510 swoord2 6511 ecopover 6579 ecopoverg 6582 endom 6709 |
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