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Mirrors > Home > MPE Home > Th. List > dfin4 | Structured version Visualization version Unicode version |
Description: Alternate definition of the intersection of two classes. Exercise 4.10(q) of [Mendelson] p. 231. (Contributed by NM, 25-Nov-2003.) |
Ref | Expression |
---|---|
dfin4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss1 3833 | . . 3 | |
2 | dfss4 3858 | . . 3 | |
3 | 1, 2 | mpbi 220 | . 2 |
4 | difin 3861 | . . 3 | |
5 | 4 | difeq2i 3725 | . 2 |
6 | 3, 5 | eqtr3i 2646 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cdif 3571 cin 3573 wss 3574 |
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-ral 2917 df-rab 2921 df-v 3202 df-dif 3577 df-in 3581 df-ss 3588 |
This theorem is referenced by: indif 3869 cnvin 5540 imain 5974 resin 6158 elcls 20877 cmmbl 23302 mbfeqalem 23409 itg1addlem4 23466 itg1addlem5 23467 inelsiga 30198 inelros 30236 topdifinffinlem 33195 poimirlem9 33418 mblfinlem4 33449 ismblfin 33450 cnambfre 33458 stoweidlem50 40267 saliincl 40545 sge0fodjrnlem 40633 meadjiunlem 40682 caragendifcl 40728 |
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