Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-dtru | Structured version Visualization version Unicode version |
Description: Remove dependency on ax-13 2246 from dtru 4857. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-dtru |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-el 32796 | . . . . 5 | |
2 | ax-nul 4789 | . . . . . 6 | |
3 | sp 2053 | . . . . . 6 | |
4 | 2, 3 | eximii 1764 | . . . . 5 |
5 | eeanv 2182 | . . . . 5 | |
6 | 1, 4, 5 | mpbir2an 955 | . . . 4 |
7 | ax9 2003 | . . . . . . 7 | |
8 | 7 | com12 32 | . . . . . 6 |
9 | 8 | con3dimp 457 | . . . . 5 |
10 | 9 | 2eximi 1763 | . . . 4 |
11 | 6, 10 | ax-mp 5 | . . 3 |
12 | equequ2 1953 | . . . . . . 7 | |
13 | 12 | notbid 308 | . . . . . 6 |
14 | ax7 1943 | . . . . . . . 8 | |
15 | 14 | con3d 148 | . . . . . . 7 |
16 | 15 | bj-spimevv 32722 | . . . . . 6 |
17 | 13, 16 | syl6bi 243 | . . . . 5 |
18 | ax7 1943 | . . . . . . . 8 | |
19 | 18 | con3d 148 | . . . . . . 7 |
20 | 19 | bj-spimevv 32722 | . . . . . 6 |
21 | 20 | a1d 25 | . . . . 5 |
22 | 17, 21 | pm2.61i 176 | . . . 4 |
23 | 22 | exlimivv 1860 | . . 3 |
24 | 11, 23 | ax-mp 5 | . 2 |
25 | exnal 1754 | . 2 | |
26 | 24, 25 | mpbi 220 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 384 wal 1481 wex 1704 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-nul 4789 ax-pow 4843 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 |
This theorem is referenced by: bj-axc16b 32798 bj-eunex 32799 bj-dtrucor 32800 bj-dvdemo1 32802 |
Copyright terms: Public domain | W3C validator |