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Mirrors > Home > MPE Home > Th. List > rspcimdv | Structured version Visualization version Unicode version |
Description: Restricted specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.) |
Ref | Expression |
---|---|
rspcimdv.1 | |
rspcimdv.2 |
Ref | Expression |
---|---|
rspcimdv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2917 | . 2 | |
2 | rspcimdv.1 | . . 3 | |
3 | simpr 477 | . . . . . . 7 | |
4 | 3 | eleq1d 2686 | . . . . . 6 |
5 | 4 | biimprd 238 | . . . . 5 |
6 | rspcimdv.2 | . . . . 5 | |
7 | 5, 6 | imim12d 81 | . . . 4 |
8 | 2, 7 | spcimdv 3290 | . . 3 |
9 | 2, 8 | mpid 44 | . 2 |
10 | 1, 9 | syl5bi 232 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wal 1481 wceq 1483 wcel 1990 wral 2912 |
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-v 3202 |
This theorem is referenced by: rspcimedv 3311 rspcdv 3312 wrd2ind 13477 mreexd 16302 mreexexlemd 16304 catcocl 16346 catass 16347 moni 16396 subccocl 16505 funcco 16531 fullfo 16572 fthf1 16577 nati 16615 acsfiindd 17177 chpscmat 20647 friendshipgt3 27256 lmxrge0 29998 funressnfv 41208 |
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