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Mirrors > Home > MPE Home > Th. List > ineqri | Structured version Visualization version Unicode version |
Description: Inference from membership to intersection. (Contributed by NM, 21-Jun-1993.) |
Ref | Expression |
---|---|
ineqri.1 |
Ref | Expression |
---|---|
ineqri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elin 3796 | . . 3 | |
2 | ineqri.1 | . . 3 | |
3 | 1, 2 | bitri 264 | . 2 |
4 | 3 | eqriv 2619 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wceq 1483 wcel 1990 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-in 3581 |
This theorem is referenced by: inidm 3822 inass 3823 dfin2 3860 indi 3873 inab 3895 in0 3968 pwin 5018 dfres3 5403 dmres 5419 inixp 33523 |
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