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Mirrors > Home > ILE Home > Th. List > ineq2d | Unicode version |
Description: Equality deduction for intersection of two classes. (Contributed by NM, 10-Apr-1994.) |
Ref | Expression |
---|---|
ineq1d.1 |
Ref | Expression |
---|---|
ineq2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ineq1d.1 | . 2 | |
2 | ineq2 3328 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1353 cin 3126 |
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 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-ext 2157 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1459 df-sb 1761 df-clab 2162 df-cleq 2168 df-clel 2171 df-nfc 2306 df-v 2737 df-in 3133 |
This theorem is referenced by: disjpr2 3653 rint0 3879 riin0 3953 disji2 3991 xpriindim 4758 riinint 4881 reseq2 4895 csbresg 4903 resindm 4942 isoselem 5811 zfz1isolem1 10786 fsumm1 11390 ennnfonelemhf1o 12379 nninfdclemcl 12414 nninfdclemp1 12416 nninfdc 12419 restval 12614 basis1 13096 baspartn 13099 eltg 13103 tgdom 13123 ntrval 13161 resttopon2 13229 restopnb 13232 qtopbasss 13572 |
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