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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 |
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breq2i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1i.1 |
. 2
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2 | breq2 4033 |
. 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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-v 2762 df-un 3157 df-sn 3624 df-pr 3625 df-op 3627 df-br 4030 |
This theorem is referenced by: breqtri 4054 en1 6853 snnen2og 6915 1nen2 6917 pm54.43 7250 caucvgprprlemval 7748 caucvgprprlemmu 7755 caucvgsr 7862 pitonnlem1 7905 lt0neg2 8488 le0neg2 8490 negap0 8649 recexaplem2 8671 recgt1 8916 crap0 8977 addltmul 9219 nn0lt10b 9397 nn0lt2 9398 3halfnz 9414 xlt0neg2 9905 xle0neg2 9907 iccshftr 10060 iccshftl 10062 iccdil 10064 icccntr 10066 fihashen1 10870 cjap0 11051 abs00ap 11206 xrmaxiflemval 11393 mertenslem2 11679 mertensabs 11680 3dvdsdec 12006 3dvds2dec 12007 ndvdsi 12074 3prm 12266 prmfac1 12290 prm23lt5 12401 sinhalfpilem 14926 sincosq1lem 14960 sincosq1sgn 14961 sincosq2sgn 14962 sincosq3sgn 14963 sincosq4sgn 14964 logrpap0b 15011 gausslemma2dlem1a 15174 2lgsoddprmlem3 15199 |
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