Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 3174 | . 2 |
4 | 1, 3 | mpbi 144 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1348 wss 3121 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-in 3127 df-ss 3134 |
This theorem is referenced by: sseqtrri 3182 eqimssi 3203 abssi 3222 ssun2 3291 inssddif 3368 difdifdirss 3499 ifidss 3541 pwundifss 4270 unixpss 4724 0ima 4971 sbthlem7 6940 ssnnctlemct 12401 toponsspwpwg 12814 eltg4i 12849 ntrss2 12915 isopn3 12919 tgioo 13340 dvfvalap 13444 dvcnp2cntop 13457 |
Copyright terms: Public domain | W3C validator |