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Mirrors > Home > MPE Home > Th. List > intmin4 | Structured version Visualization version Unicode version |
Description: Elimination of a conjunct in a class intersection. (Contributed by NM, 31-Jul-2006.) |
Ref | Expression |
---|---|
intmin4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssintab 4494 | . . . 4 | |
2 | simpr 477 | . . . . . . . 8 | |
3 | ancr 572 | . . . . . . . 8 | |
4 | 2, 3 | impbid2 216 | . . . . . . 7 |
5 | 4 | imbi1d 331 | . . . . . 6 |
6 | 5 | alimi 1739 | . . . . 5 |
7 | albi 1746 | . . . . 5 | |
8 | 6, 7 | syl 17 | . . . 4 |
9 | 1, 8 | sylbi 207 | . . 3 |
10 | vex 3203 | . . . 4 | |
11 | 10 | elintab 4487 | . . 3 |
12 | 10 | elintab 4487 | . . 3 |
13 | 9, 11, 12 | 3bitr4g 303 | . 2 |
14 | 13 | eqrdv 2620 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wceq 1483 wcel 1990 cab 2608 wss 3574 cint 4475 |
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-v 3202 df-in 3581 df-ss 3588 df-int 4476 |
This theorem is referenced by: (None) |
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