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Mirrors > Home > MPE Home > Th. List > rspce | Structured version Visualization version Unicode version |
Description: Restricted existential specialization, using implicit substitution. (Contributed by NM, 26-May-1998.) (Revised by Mario Carneiro, 11-Oct-2016.) |
Ref | Expression |
---|---|
rspc.1 | |
rspc.2 |
Ref | Expression |
---|---|
rspce |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2764 | . . . 4 | |
2 | nfv 1843 | . . . . 5 | |
3 | rspc.1 | . . . . 5 | |
4 | 2, 3 | nfan 1828 | . . . 4 |
5 | eleq1 2689 | . . . . 5 | |
6 | rspc.2 | . . . . 5 | |
7 | 5, 6 | anbi12d 747 | . . . 4 |
8 | 1, 4, 7 | spcegf 3289 | . . 3 |
9 | 8 | anabsi5 858 | . 2 |
10 | df-rex 2918 | . 2 | |
11 | 9, 10 | sylibr 224 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wnf 1708 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-rex 2918 df-v 3202 |
This theorem is referenced by: rspcev 3309 ac6c4 9303 fsumcom2OLD 14506 infcvgaux1i 14589 fprodcom2OLD 14715 iunmbl2 23325 esumcvg 30148 ptrecube 33409 poimirlem24 33433 sdclem1 33539 uzwo4 39221 eliuniincex 39292 wessf1ornlem 39371 elrnmpt1sf 39376 iuneqfzuzlem 39550 uzublem 39657 uzub 39658 limsuppnfdlem 39933 limsupubuzlem 39944 sge0gerp 40612 smflim 40985 |
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