Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > intss1 | Unicode version |
Description: An element of a class includes the intersection of the class. Exercise 4 of [TakeutiZaring] p. 44 (with correction), generalized to classes. (Contributed by NM, 18-Nov-1995.) |
Ref | Expression |
---|---|
intss1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2733 | . . . 4 | |
2 | 1 | elint 3837 | . . 3 |
3 | eleq1 2233 | . . . . . 6 | |
4 | eleq2 2234 | . . . . . 6 | |
5 | 3, 4 | imbi12d 233 | . . . . 5 |
6 | 5 | spcgv 2817 | . . . 4 |
7 | 6 | pm2.43a 51 | . . 3 |
8 | 2, 7 | syl5bi 151 | . 2 |
9 | 8 | ssrdv 3153 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1346 wceq 1348 wcel 2141 wss 3121 cint 3831 |
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-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-in 3127 df-ss 3134 df-int 3832 |
This theorem is referenced by: intminss 3856 intmin3 3858 intab 3860 int0el 3861 trintssm 4103 inteximm 4135 onnmin 4552 peano5 4582 peano5nnnn 7854 peano5nni 8881 dfuzi 9322 bj-intabssel 13824 bj-intabssel1 13825 |
Copyright terms: Public domain | W3C validator |