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Mirrors > Home > ILE Home > Th. List > eqbrtrrd | Unicode version |
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 24-Oct-1999.) |
Ref | Expression |
---|---|
eqbrtrrd.1 | |
eqbrtrrd.2 |
Ref | Expression |
---|---|
eqbrtrrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqbrtrrd.1 | . . 3 | |
2 | 1 | eqcomd 2086 | . 2 |
3 | eqbrtrrd.2 | . 2 | |
4 | 2, 3 | eqbrtrd 3805 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 class class class wbr 3785 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-un 2977 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 |
This theorem is referenced by: dftpos4 5901 phpm 6351 unsnfidcex 6385 prmuloclemcalc 6755 mullocprlem 6760 cauappcvgprlemladdfl 6845 caucvgprlemopl 6859 caucvgprprlemloccalc 6874 caucvgprprlemopl 6887 ltadd1sr 6953 axarch 7057 lemulge11 7944 modqmuladdim 9369 ltexp2a 9528 leexp2a 9529 nnlesq 9578 faclbnd6 9671 facavg 9673 cvg1nlemcxze 9868 resqrexlemover 9896 resqrexlemlo 9899 resqrexlemnmsq 9903 resqrexlemnm 9904 leabs 9960 abs3dif 9991 abs2dif 9992 maxabslemlub 10093 maxltsup 10104 recn2 10155 imcn2 10156 iiserex 10177 divalglemnqt 10320 mulgcd 10405 dvdssqlem 10419 nn0seqcvgd 10423 mulgcddvds 10476 rpdvds 10481 pw2dvdseulemle 10545 sqrt2irraplemnn 10557 |
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