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Mirrors > Home > MPE Home > Th. List > uneqri | Structured version Visualization version Unicode version |
Description: Inference from membership to union. (Contributed by NM, 21-Jun-1993.) |
Ref | Expression |
---|---|
uneqri.1 |
Ref | Expression |
---|---|
uneqri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elun 3753 | . . 3 | |
2 | uneqri.1 | . . 3 | |
3 | 1, 2 | bitri 264 | . 2 |
4 | 3 | eqriv 2619 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wo 383 wceq 1483 wcel 1990 cun 3572 |
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-un 3579 |
This theorem is referenced by: unidm 3756 uncom 3757 unass 3770 dfun2 3859 undi 3874 unab 3894 un0 3967 inundif 4046 |
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