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Mirrors > Home > ILE Home > Th. List > 3brtr4d | Unicode version |
Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 21-Feb-2005.) |
Ref | Expression |
---|---|
3brtr4d.1 | |
3brtr4d.2 | |
3brtr4d.3 |
Ref | Expression |
---|---|
3brtr4d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3brtr4d.1 | . 2 | |
2 | 3brtr4d.2 | . . 3 | |
3 | 3brtr4d.3 | . . 3 | |
4 | 2, 3 | breq12d 3777 | . 2 |
5 | 1, 4 | mpbird 156 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 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: f1oiso2 5466 prarloclemarch2 6517 caucvgprprlemmu 6793 caucvgsrlembound 6878 mulap0 7635 lediv12a 7860 recp1lt1 7865 fldiv4p1lem1div2 9147 intfracq 9162 modqmulnn 9184 frecfzennn 9203 monoord2 9236 expgt1 9293 leexp2r 9308 leexp1a 9309 bernneq 9369 sqrtgt0 9632 absrele 9679 absimle 9680 abstri 9700 abs2difabs 9704 climsqz 9855 climsqz2 9856 |
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