![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > eqbrtrri | Unicode version |
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eqbrtrr.1 |
![]() ![]() ![]() ![]() |
eqbrtrr.2 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
eqbrtrri |
![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqbrtrr.1 |
. . 3
![]() ![]() ![]() ![]() | |
2 | 1 | eqcomi 2181 |
. 2
![]() ![]() ![]() ![]() |
3 | eqbrtrr.2 |
. 2
![]() ![]() ![]() ![]() | |
4 | 2, 3 | eqbrtri 4021 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-sn 3597 df-pr 3598 df-op 3600 df-br 4001 |
This theorem is referenced by: 3brtr3i 4029 dju1p1e2 7189 expnass 10598 sqrt2gt1lt2 11029 cos1bnd 11738 cos2bnd 11739 infpn2 12427 2strstr1g 12546 coseq00topi 13889 pigt3 13898 |
Copyright terms: Public domain | W3C validator |