Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > disjel | Unicode version |
Description: A set can't belong to both members of disjoint classes. (Contributed by NM, 28-Feb-2015.) |
Ref | Expression |
---|---|
disjel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | disj3 3410 | . . 3 | |
2 | eleq2 2201 | . . . 4 | |
3 | eldifn 3194 | . . . 4 | |
4 | 2, 3 | syl6bi 162 | . . 3 |
5 | 1, 4 | sylbi 120 | . 2 |
6 | 5 | imp 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wceq 1331 wcel 1480 cdif 3063 cin 3065 c0 3358 |
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-in1 603 ax-in2 604 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 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-v 2683 df-dif 3068 df-in 3072 df-nul 3359 |
This theorem is referenced by: fvun1 5480 ctssdccl 6989 fsumsplit 11169 |
Copyright terms: Public domain | W3C validator |