![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 3sstr4d | Unicode version |
Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 30-Nov-1995.) (Proof shortened by Eric Schmidt, 26-Jan-2007.) |
Ref | Expression |
---|---|
3sstr4d.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3sstr4d.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3sstr4d.3 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
3sstr4d |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3sstr4d.1 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 3sstr4d.2 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 3sstr4d.3 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 2, 3 | sseq12d 3201 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 1, 4 | mpbird 167 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-in 3150 df-ss 3157 |
This theorem is referenced by: rdgss 6407 sucinc2 6470 oawordi 6493 nnnninf 7153 fzoss1 10200 fzoss2 10201 lspss 13712 clsss 14070 ntrss 14071 sslm 14199 txss12 14218 metss2lem 14449 xmettxlem 14461 xmettx 14462 nnsf 15208 nninfself 15216 |
Copyright terms: Public domain | W3C validator |