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Mirrors > Home > ILE Home > Th. List > breqtrri | Unicode version |
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
breqtrr.1 | |
breqtrr.2 |
Ref | Expression |
---|---|
breqtrri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breqtrr.1 | . 2 | |
2 | breqtrr.2 | . . 3 | |
3 | 2 | eqcomi 2044 | . 2 |
4 | 1, 3 | breqtri 3787 | 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: 3brtr4i 3792 ensn1 6276 0lt1sr 6850 0le2 8006 2pos 8007 3pos 8010 4pos 8013 5pos 8016 6pos 8017 7pos 8018 8pos 8019 9pos 8020 10pos 8021 1lt2 8086 2lt3 8087 3lt4 8089 4lt5 8092 5lt6 8096 6lt7 8101 7lt8 8107 8lt9 8114 9lt10 8122 nn0le2xi 8232 numltc 8387 declti 8392 sqge0i 9340 ex-fl 9895 |
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