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Mirrors > Home > NFE Home > Th. List > rspcimdv | 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 2619 | . 2 | |
2 | rspcimdv.1 | . . 3 | |
3 | simpr 447 | . . . . . . 7 | |
4 | 3 | eleq1d 2419 | . . . . . 6 |
5 | 4 | biimprd 214 | . . . . 5 |
6 | rspcimdv.2 | . . . . 5 | |
7 | 5, 6 | imim12d 68 | . . . 4 |
8 | 2, 7 | spcimdv 2936 | . . 3 |
9 | 2, 8 | mpid 37 | . 2 |
10 | 1, 9 | syl5bi 208 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 wal 1540 wceq 1642 wcel 1710 wral 2614 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-v 2861 |
This theorem is referenced by: rspcimedv 2957 rspcdv 2958 |
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