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Mirrors > Home > MPE Home > Th. List > prnz | Structured version Visualization version Unicode version |
Description: A pair containing a set is not empty. (Contributed by NM, 9-Apr-1994.) |
Ref | Expression |
---|---|
prnz.1 |
Ref | Expression |
---|---|
prnz |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prnz.1 | . . 3 | |
2 | 1 | prid1 4297 | . 2 |
3 | 2 | ne0ii 3923 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1990 wne 2794 cvv 3200 c0 3915 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-dif 3577 df-un 3579 df-nul 3916 df-sn 4178 df-pr 4180 |
This theorem is referenced by: prnzgOLD 4312 opnz 4942 propssopi 4971 fiint 8237 wilthlem2 24795 upgrbi 25988 wlkvtxiedg 26520 shincli 28221 chincli 28319 spr0nelg 41726 sprvalpwn0 41733 |
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