Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > difin | Structured version Visualization version Unicode version |
Description: Difference with intersection. Theorem 33 of [Suppes] p. 29. (Contributed by NM, 31-Mar-1998.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
difin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.61 442 | . . 3 | |
2 | anclb 570 | . . . . 5 | |
3 | elin 3796 | . . . . . 6 | |
4 | 3 | imbi2i 326 | . . . . 5 |
5 | iman 440 | . . . . 5 | |
6 | 2, 4, 5 | 3bitr2i 288 | . . . 4 |
7 | 6 | con2bii 347 | . . 3 |
8 | eldif 3584 | . . 3 | |
9 | 1, 7, 8 | 3bitr4i 292 | . 2 |
10 | 9 | difeqri 3730 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 384 wceq 1483 wcel 1990 cdif 3571 cin 3573 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-dif 3577 df-in 3581 |
This theorem is referenced by: dfin4 3867 indif 3869 dfsymdif3 3893 notrab 3904 disjdif2 4047 dfsdom2 8083 hashdif 13201 isercolllem3 14397 iuncld 20849 llycmpkgen2 21353 1stckgen 21357 txkgen 21455 cmmbl 23302 disjdifprg2 29389 ldgenpisyslem1 30226 onint1 32448 nonrel 37890 nzprmdif 38518 |
Copyright terms: Public domain | W3C validator |