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Mirrors > Home > MPE Home > Th. List > prneli | 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, using . (Contributed by David A. Wheeler, 10-May-2015.) |
Ref | Expression |
---|---|
prneli.1 | |
prneli.2 |
Ref | Expression |
---|---|
prneli |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prneli.1 | . . 3 | |
2 | prneli.2 | . . 3 | |
3 | 1, 2 | nelpri 4201 | . 2 |
4 | 3 | nelir 2900 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wne 2794 wnel 2897 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-nel 2898 df-v 3202 df-un 3579 df-sn 4178 df-pr 4180 |
This theorem is referenced by: vdegp1ai 26432 |
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