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| Description: Deduction version of hbcsb1g 2067. |
| Ref | Expression |
|---|---|
| hbcsb1gd.1 |
|
| hbcsb1gd.2 |
|
| Ref | Expression |
|---|---|
| hbcsb1gd |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hbcsb1gd.1 |
. . . . . 6
| |
| 2 | 1 | a1d 12 |
. . . . 5
|
| 3 | hbcsb1gd.2 |
. . . . . 6
| |
| 4 | ax-17 1003 |
. . . . . . 7
| |
| 5 | 4 | a1i 8 |
. . . . . 6
|
| 6 | 1, 3, 5 | hbeld 1952 |
. . . . 5
|
| 7 | 2, 6 | hband 1143 |
. . . 4
|
| 8 | 7 | anabsi5 497 |
. . 3
|
| 9 | ax-17 1003 |
. . . 4
| |
| 10 | 9 | a1i 8 |
. . 3
|
| 11 | 1, 3 | hbsbc1gd 2023 |
. . . 4
|
| 12 | sbcel2g 2058 |
. . . . 5
| |
| 13 | 12 | adantl 388 |
. . . 4
|
| 14 | 8, 13 | albid 1136 |
. . . 4
|
| 15 | 11, 13, 14 | 3imtr3d 544 |
. . 3
|
| 16 | 8, 10, 15 | hbeld 1952 |
. 2
|
| 17 | elisset 1855 |
. 2
| |
| 18 | 16, 17 | sylan2 453 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem is referenced by: csbnest1g 2081 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 994 ax-gen 995 ax-8 996 ax-9 997 ax-10 998 ax-11 999 ax-12 1000 ax-17 1003 ax-4 1005 ax-5o 1007 ax-6o 1010 ax-9o 1155 ax-10o 1173 ax-16 1243 ax-11o 1251 ax-ext 1494 |
| This theorem depends on definitions: df-bi 145 df-or 222 df-an 223 df-3an 780 df-ex 1013 df-sb 1205 df-clab 1500 df-cleq 1505 df-clel 1508 df-v 1850 df-sbc 1979 df-csb 2044 |