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Mirrors > Home > MPE Home > Th. List > difin0 | Structured version Visualization version Unicode version |
Description: The difference of a class from its intersection is empty. Theorem 37 of [Suppes] p. 29. (Contributed by NM, 17-Aug-2004.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
difin0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss2 3834 | . 2 | |
2 | ssdif0 3942 | . 2 | |
3 | 1, 2 | mpbi 220 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cdif 3571 cin 3573 wss 3574 c0 3915 |
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 df-ss 3588 df-nul 3916 |
This theorem is referenced by: volinun 23314 |
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