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Mirrors > Home > MPE Home > Th. List > rexsng | Structured version Visualization version Unicode version |
Description: Restricted existential quantification over a singleton. (Contributed by NM, 29-Jan-2012.) |
Ref | Expression |
---|---|
ralsng.1 |
Ref | Expression |
---|---|
rexsng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexsns 4217 | . 2 | |
2 | ralsng.1 | . . 3 | |
3 | 2 | sbcieg 3468 | . 2 |
4 | 1, 3 | syl5bb 272 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wceq 1483 wcel 1990 wrex 2913 wsbc 3435 csn 4177 |
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-3an 1039 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-rex 2918 df-v 3202 df-sbc 3436 df-sn 4178 |
This theorem is referenced by: rexsn 4223 rexprg 4235 rextpg 4237 iunxsng 4602 frirr 5091 frsn 5189 imasng 5487 scshwfzeqfzo 13572 dvdsprmpweqnn 15589 mnd1 17331 grp1 17522 1loopgrvd0 26400 1egrvtxdg0 26407 nfrgr2v 27136 1vwmgr 27140 ballotlemfc0 30554 ballotlemfcc 30555 bj-restsn 33035 elpaddat 35090 elpadd2at 35092 brfvidRP 37980 iccelpart 41369 zlidlring 41928 lco0 42216 |
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