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Mirrors > Home > ILE Home > Th. List > spsbim | Unicode version |
Description: Specialization of implication. (Contributed by NM, 5-Aug-1993.) (Proof rewritten by Jim Kingdon, 21-Jan-2018.) |
Ref | Expression |
---|---|
spsbim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imim2 49 | . . . 4 | |
2 | 1 | sps 1430 | . . 3 |
3 | id 19 | . . . . . 6 | |
4 | 3 | anim2d 320 | . . . . 5 |
5 | 4 | alimi 1344 | . . . 4 |
6 | exim 1490 | . . . 4 | |
7 | 5, 6 | syl 14 | . . 3 |
8 | 2, 7 | anim12d 318 | . 2 |
9 | df-sb 1646 | . 2 | |
10 | df-sb 1646 | . 2 | |
11 | 8, 9, 10 | 3imtr4g 194 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wal 1241 wex 1381 wsb 1645 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-sb 1646 |
This theorem is referenced by: spsbbi 1725 hbsb4t 1889 moim 1964 |
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