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Mirrors > Home > ILE Home > Th. List > breqtri | Unicode version |
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
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breqtr.1 |
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breqtr.2 |
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Ref | Expression |
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breqtri |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breqtr.1 |
. 2
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2 | breqtr.2 |
. . 3
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3 | 2 | breq2i 4008 |
. 2
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4 | 1, 3 | mpbi 145 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-sn 3597 df-pr 3598 df-op 3600 df-br 4001 |
This theorem is referenced by: breqtrri 4027 3brtr3i 4029 le9lt10 9399 9lt10 9503 sqrt2gt1lt2 11042 trireciplem 11492 cos1bnd 11751 cos2bnd 11752 cos01gt0 11754 sin4lt0 11758 z4even 11904 coseq00topi 13923 sincos4thpi 13928 lgsdir2lem2 14097 lgsdir2lem3 14098 ex-fl 14133 |
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