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Mirrors > Home > ILE Home > Th. List > sseqtri | Unicode version |
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 28-Jul-1995.) |
Ref | Expression |
---|---|
sseqtr.1 | |
sseqtr.2 |
Ref | Expression |
---|---|
sseqtri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseqtr.1 | . 2 | |
2 | sseqtr.2 | . . 3 | |
3 | 2 | sseq2i 3155 | . 2 |
4 | 1, 3 | mpbi 144 | 1 |
Colors of variables: wff set class |
Syntax hints: 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: sseqtrri 3163 eqimssi 3184 abssi 3203 ssun2 3271 inssddif 3348 difdifdirss 3478 ifidss 3520 pwundifss 4246 unixpss 4700 0ima 4947 sbthlem7 6908 ssnnctlemct 12217 toponsspwpwg 12462 eltg4i 12497 ntrss2 12563 isopn3 12567 tgioo 12988 dvfvalap 13092 dvcnp2cntop 13105 |
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