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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 3271 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 cin 3070 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-in 3077 |
This theorem is referenced by: disjpr2 3587 rint0 3810 riin0 3884 disji2 3922 xpriindim 4677 riinint 4800 reseq2 4814 csbresg 4822 resindm 4861 isoselem 5721 zfz1isolem1 10583 fsumm1 11185 ennnfonelemhf1o 11926 restval 12126 basis1 12214 baspartn 12217 eltg 12221 tgdom 12241 ntrval 12279 resttopon2 12347 restopnb 12350 qtopbasss 12690 |
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