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Mirrors > Home > ILE Home > Th. List > difidALT | Unicode version |
Description: The difference between a class and itself is the empty set. Proposition 5.15 of [TakeutiZaring] p. 20. Also Theorem 32 of [Suppes] p. 28. Alternate proof of difid 3401. (Contributed by David Abernethy, 17-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
difidALT |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfdif2 3049 | . 2 | |
2 | dfnul3 3336 | . 2 | |
3 | 1, 2 | eqtr4i 2141 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wceq 1316 wcel 1465 crab 2397 cdif 3038 c0 3333 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rab 2402 df-v 2662 df-dif 3043 df-nul 3334 |
This theorem is referenced by: (None) |
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