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Mirrors > Home > ILE Home > Th. List > 3brtr4i | Unicode version |
Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999.) |
Ref | Expression |
---|---|
3brtr4.1 | |
3brtr4.2 | |
3brtr4.3 |
Ref | Expression |
---|---|
3brtr4i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3brtr4.2 | . . 3 | |
2 | 3brtr4.1 | . . 3 | |
3 | 1, 2 | eqbrtri 3783 | . 2 |
4 | 3brtr4.3 | . 2 | |
5 | 3, 4 | breqtrri 3789 | 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: 1lt2nq 6504 0lt1sr 6850 ax0lt1 6950 ax-0lt1 6990 declt 8388 decltc 8389 frecfzennn 9203 |
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