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Mirrors > Home > ILE Home > Th. List > breq2i | Unicode version |
Description: Equality inference for a binary relation. (Contributed by NM, 8-Feb-1996.) |
Ref | Expression |
---|---|
breq1i.1 |
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Ref | Expression |
---|---|
breq2i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1i.1 |
. 2
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2 | breq2 4004 |
. 2
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3 | 1, 2 | ax-mp 5 |
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: breqtri 4025 en1 6792 snnen2og 6852 1nen2 6854 pm54.43 7182 caucvgprprlemval 7665 caucvgprprlemmu 7672 caucvgsr 7779 pitonnlem1 7822 lt0neg2 8403 le0neg2 8405 negap0 8564 recexaplem2 8585 recgt1 8830 crap0 8891 addltmul 9131 nn0lt10b 9309 nn0lt2 9310 3halfnz 9326 xlt0neg2 9813 xle0neg2 9815 iccshftr 9968 iccshftl 9970 iccdil 9972 icccntr 9974 fihashen1 10750 cjap0 10887 abs00ap 11042 xrmaxiflemval 11229 mertenslem2 11515 mertensabs 11516 3dvdsdec 11840 3dvds2dec 11841 ndvdsi 11908 3prm 12098 prmfac1 12122 prm23lt5 12233 sinhalfpilem 13845 sincosq1lem 13879 sincosq1sgn 13880 sincosq2sgn 13881 sincosq3sgn 13882 sincosq4sgn 13883 logrpap0b 13930 |
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