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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 54 | . . . 4 | |
2 | 1 | sps 1470 | . . 3 |
3 | id 19 | . . . . . 6 | |
4 | 3 | anim2d 330 | . . . . 5 |
5 | 4 | alimi 1384 | . . . 4 |
6 | exim 1530 | . . . 4 | |
7 | 5, 6 | syl 14 | . . 3 |
8 | 2, 7 | anim12d 328 | . 2 |
9 | df-sb 1686 | . 2 | |
10 | df-sb 1686 | . 2 | |
11 | 8, 9, 10 | 3imtr4g 203 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wal 1282 wex 1421 wsb 1685 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 df-sb 1686 |
This theorem is referenced by: spsbbi 1765 hbsb4t 1930 moim 2005 |
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