Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > eqbrtri | Unicode version |
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eqbrtr.1 | |
eqbrtr.2 |
Ref | Expression |
---|---|
eqbrtri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqbrtr.2 | . 2 | |
2 | eqbrtr.1 | . . 3 | |
3 | 2 | breq1i 3771 | . 2 |
4 | 1, 3 | mpbir 134 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 class class class wbr 3764 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 |
This theorem is referenced by: eqbrtrri 3785 3brtr4i 3792 neg1lt0 8025 halflt1 8142 numlti 8391 ex-fl 9895 |
Copyright terms: Public domain | W3C validator |