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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 3120 | . 2 |
5 | 1, 4 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wss 3066 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-in 3072 df-ss 3079 |
This theorem is referenced by: rabss2 3175 unss2 3242 sslin 3297 ssopab2 4192 xpss12 4641 coss1 4689 coss2 4690 cnvss 4707 rnss 4764 ssres 4840 ssres2 4841 imass1 4909 imass2 4910 imadif 5198 imain 5200 ssoprab2 5820 suppssfv 5971 suppssov1 5972 tposss 6136 ss2ixp 6598 isumsplit 11253 isumrpcl 11256 |
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