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Mirrors > Home > NFE Home > Th. List > sbccomlem | Unicode version |
Description: Lemma for sbccom 3117. (Contributed by NM, 14-Nov-2005.) (Revised by Mario Carneiro, 18-Oct-2016.) |
Ref | Expression |
---|---|
sbccomlem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1741 | . . . 4 | |
2 | exdistr 1906 | . . . 4 | |
3 | an12 772 | . . . . . . 7 | |
4 | 3 | exbii 1582 | . . . . . 6 |
5 | 19.42v 1905 | . . . . . 6 | |
6 | 4, 5 | bitri 240 | . . . . 5 |
7 | 6 | exbii 1582 | . . . 4 |
8 | 1, 2, 7 | 3bitr3i 266 | . . 3 |
9 | sbc5 3070 | . . 3 | |
10 | sbc5 3070 | . . 3 | |
11 | 8, 9, 10 | 3bitr4i 268 | . 2 |
12 | sbc5 3070 | . . 3 | |
13 | 12 | sbcbii 3101 | . 2 |
14 | sbc5 3070 | . . 3 | |
15 | 14 | sbcbii 3101 | . 2 |
16 | 11, 13, 15 | 3bitr4i 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wa 358 wex 1541 wceq 1642 wsbc 3046 |
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-v 2861 df-sbc 3047 |
This theorem is referenced by: sbccom 3117 |
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