Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sseq12i | Unicode version |
Description: An equality inference for the subclass relationship. (Contributed by NM, 31-May-1999.) (Proof shortened by Eric Schmidt, 26-Jan-2007.) |
Ref | Expression |
---|---|
sseq1i.1 | |
sseq12i.2 |
Ref | Expression |
---|---|
sseq12i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1i.1 | . 2 | |
2 | sseq12i.2 | . 2 | |
3 | sseq12 3117 | . 2 | |
4 | 1, 2, 3 | mp2an 422 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 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: 3sstr3i 3132 3sstr4i 3133 3sstr3g 3134 3sstr4g 3135 ss2rab 3168 |
Copyright terms: Public domain | W3C validator |