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Mirrors > Home > MPE Home > Th. List > nelprd | Structured version Visualization version Unicode version |
Description: If an element doesn't match the items in an unordered pair, it is not in the unordered pair, deduction version. (Contributed by Alexander van der Vekens, 25-Jan-2018.) |
Ref | Expression |
---|---|
nelprd.1 | |
nelprd.2 |
Ref | Expression |
---|---|
nelprd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nelprd.1 | . 2 | |
2 | nelprd.2 | . 2 | |
3 | neanior 2886 | . . 3 | |
4 | elpri 4197 | . . . 4 | |
5 | 4 | con3i 150 | . . 3 |
6 | 3, 5 | sylbi 207 | . 2 |
7 | 1, 2, 6 | syl2anc 693 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wo 383 wa 384 wceq 1483 wcel 1990 wne 2794 cpr 4179 |
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-ne 2795 df-v 3202 df-un 3579 df-sn 4178 df-pr 4180 |
This theorem is referenced by: renfdisj 10098 sumtp 14478 pmtrprfv3 17874 perfectlem2 24955 nbupgrres 26266 usgr2pthlem 26659 eupth2lem3lem6 27093 perfectALTVlem2 41631 |
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