![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > ecelqsi | Unicode version |
Description: Membership of an equivalence class in a quotient set. (Contributed by NM, 25-Jul-1995.) (Revised by Mario Carneiro, 9-Jul-2014.) |
Ref | Expression |
---|---|
ecelqsi.1 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
ecelqsi |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ecelqsi.1 |
. 2
![]() ![]() ![]() ![]() | |
2 | ecelqsg 6345 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | mpan 415 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-pow 4009 ax-pr 4036 ax-un 4260 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-v 2621 df-un 3003 df-in 3005 df-ss 3012 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-br 3846 df-opab 3900 df-xp 4444 df-cnv 4446 df-dm 4448 df-rn 4449 df-res 4450 df-ima 4451 df-ec 6294 df-qs 6298 |
This theorem is referenced by: ecopqsi 6347 th3q 6397 1nq 6925 addclnq 6934 mulclnq 6935 recexnq 6949 ltexnqq 6967 prarloclemarch 6977 prarloclemarch2 6978 nnnq 6981 nqnq0 7000 addnnnq0 7008 mulnnnq0 7009 addclnq0 7010 mulclnq0 7011 nqpnq0nq 7012 prarloclemlt 7052 prarloclemlo 7053 prarloclemcalc 7061 nqprm 7101 addsrpr 7291 mulsrpr 7292 0r 7296 1sr 7297 m1r 7298 addclsr 7299 mulclsr 7300 prsrcl 7329 pitonnlem2 7384 pitonn 7385 pitore 7387 recnnre 7388 |
Copyright terms: Public domain | W3C validator |