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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 3119 | . 2 |
4 | 1, 3 | mpbi 144 | 1 |
Colors of variables: wff set class |
Syntax hints: 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: sseqtrri 3127 eqimssi 3148 abssi 3167 ssun2 3235 inssddif 3312 difdifdirss 3442 pwundifss 4202 unixpss 4647 0ima 4894 sbthlem7 6844 toponsspwpwg 12178 eltg4i 12213 ntrss2 12279 isopn3 12283 tgioo 12704 dvfvalap 12808 dvcnp2cntop 12821 |
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