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Mirrors > Home > ILE Home > Th. List > breq1i | Unicode version |
Description: Equality inference for a binary relation. (Contributed by NM, 8-Feb-1996.) |
Ref | Expression |
---|---|
breq1i.1 |
Ref | Expression |
---|---|
breq1i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1i.1 | . 2 | |
2 | breq1 3992 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1348 class class class wbr 3989 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 |
This theorem is referenced by: eqbrtri 4010 brtpos0 6231 euen1 6780 euen1b 6781 2dom 6783 infglbti 7002 pr2nelem 7168 caucvgprprlemnbj 7655 caucvgprprlemmu 7657 caucvgprprlemaddq 7670 caucvgprprlem1 7671 gt0srpr 7710 caucvgsr 7764 mappsrprg 7766 map2psrprg 7767 pitonnlem1 7807 pitoregt0 7811 axprecex 7842 axpre-mulgt0 7849 axcaucvglemres 7861 lt0neg1 8387 le0neg1 8389 reclt1 8812 addltmul 9114 eluz2b1 9560 nn01to3 9576 xlt0neg1 9795 xle0neg1 9797 iccshftr 9951 iccshftl 9953 iccdil 9955 icccntr 9957 bernneq 10596 cbvsum 11323 expcnv 11467 cbvprod 11521 oddge22np1 11840 nn0o1gt2 11864 isprm3 12072 dvdsnprmd 12079 pw2dvdslemn 12119 txmetcnp 13312 sincosq1sgn 13541 sincosq3sgn 13543 sincosq4sgn 13544 logrpap0b 13591 |
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