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Mirrors > Home > ILE Home > Th. List > 3sstr4g | Unicode version |
Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Eric Schmidt, 26-Jan-2007.) |
Ref | Expression |
---|---|
3sstr4g.1 | |
3sstr4g.2 | |
3sstr4g.3 |
Ref | Expression |
---|---|
3sstr4g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3sstr4g.1 | . 2 | |
2 | 3sstr4g.2 | . . 3 | |
3 | 3sstr4g.3 | . . 3 | |
4 | 2, 3 | sseq12i 3156 | . 2 |
5 | 1, 4 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wss 3102 |
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-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-in 3108 df-ss 3115 |
This theorem is referenced by: rabss2 3211 unss2 3278 sslin 3333 ssopab2 4235 xpss12 4693 coss1 4741 coss2 4742 cnvss 4759 rnss 4816 ssres 4892 ssres2 4893 imass1 4961 imass2 4962 imadif 5250 imain 5252 ssoprab2 5877 suppssfv 6028 suppssov1 6029 tposss 6193 ss2ixp 6656 isumsplit 11388 isumrpcl 11391 |
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