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Mirrors > Home > ILE Home > Th. List > ineq12d | Unicode version |
Description: Equality deduction for intersection of two classes. (Contributed by NM, 24-Jun-2004.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
ineq1d.1 | |
ineq12d.2 |
Ref | Expression |
---|---|
ineq12d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ineq1d.1 | . 2 | |
2 | ineq12d.2 | . 2 | |
3 | ineq12 3272 | . 2 | |
4 | 1, 2, 3 | syl2anc 408 | 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: csbing 3283 funprg 5173 funtpg 5174 offval 5989 ofrfval 5990 undifdc 6812 djudom 6978 ressid2 12018 ressval2 12019 |
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