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Mirrors > Home > ILE Home > Th. List > hbsbd | Unicode version |
Description: Deduction version of hbsb 1922. (Contributed by NM, 15-Feb-2013.) (Proof rewritten by Jim Kingdon, 23-Mar-2018.) |
Ref | Expression |
---|---|
hbsbd.1 | |
hbsbd.2 | |
hbsbd.3 |
Ref | Expression |
---|---|
hbsbd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbsbd.2 | . . . 4 | |
2 | 1 | nfi 1438 | . . 3 |
3 | hbsbd.3 | . . . . . . 7 | |
4 | 1, 3 | nfdh 1504 | . . . . . 6 |
5 | 2, 4 | nfim1 1550 | . . . . 5 |
6 | 5 | nfsb 1919 | . . . 4 |
7 | hbsbd.1 | . . . . . 6 | |
8 | 7 | sbrim 1929 | . . . . 5 |
9 | 8 | nfbii 1449 | . . . 4 |
10 | 6, 9 | mpbi 144 | . . 3 |
11 | 2, 10 | nfrimi 1505 | . 2 |
12 | 11 | nfrd 1500 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1329 wnf 1436 wsb 1735 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 |
This theorem is referenced by: (None) |
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