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Mirrors > Home > MPE Home > Th. List > rspcedv | Structured version Visualization version Unicode version |
Description: Restricted existential specialization, using implicit substitution. (Contributed by FL, 17-Apr-2007.) (Revised by Mario Carneiro, 4-Jan-2017.) |
Ref | Expression |
---|---|
rspcdv.1 | |
rspcdv.2 |
Ref | Expression |
---|---|
rspcedv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspcdv.1 | . 2 | |
2 | rspcdv.2 | . . 3 | |
3 | 2 | biimprd 238 | . 2 |
4 | 1, 3 | rspcimedv 3311 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wrex 2913 |
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-ral 2917 df-rex 2918 df-v 3202 |
This theorem is referenced by: rspcebdv 3314 rspcedvd 3317 fsuppmapnn0fiubOLD 12791 wrdl1exs1 13393 0csh0 13539 gcdcllem1 15221 nn0gsumfz 18380 pmatcollpw3lem 20588 pmatcollpw3fi1lem2 20592 pm2mpfo 20619 f1otrg 25751 cusgrfilem2 26352 wwlksnredwwlkn 26790 wwlksnextprop 26807 clwwlksnun 26974 cusconngr 27051 xrofsup 29533 esum2d 30155 rexzrexnn0 37368 ov2ssiunov2 37992 lcoel0 42217 lcoss 42225 el0ldep 42255 ldepspr 42262 islindeps2 42272 isldepslvec2 42274 |
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