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Mirrors > Home > MPE Home > Th. List > Mathboxes > arg-ax | Structured version Visualization version Unicode version |
Description: ? (Contributed by Anthony Hart, 14-Aug-2011.) |
Ref | Expression |
---|---|
arg-ax |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nan 1448 | . . . . 5 | |
2 | pm4.57 518 | . . . . . . . 8 | |
3 | orel2 398 | . . . . . . . . . . . . 13 | |
4 | 3 | com12 32 | . . . . . . . . . . . 12 |
5 | simpr 477 | . . . . . . . . . . . . 13 | |
6 | 5 | a1i 11 | . . . . . . . . . . . 12 |
7 | 4, 6 | jad 174 | . . . . . . . . . . 11 |
8 | 7 | com12 32 | . . . . . . . . . 10 |
9 | pm3.45 879 | . . . . . . . . . . . 12 | |
10 | pm3.45 879 | . . . . . . . . . . . 12 | |
11 | 9, 10 | anim12i 590 | . . . . . . . . . . 11 |
12 | jaob 822 | . . . . . . . . . . 11 | |
13 | jaob 822 | . . . . . . . . . . 11 | |
14 | 11, 12, 13 | 3imtr4i 281 | . . . . . . . . . 10 |
15 | 8, 14 | syl 17 | . . . . . . . . 9 |
16 | pm3.22 465 | . . . . . . . . 9 | |
17 | 15, 16 | syl6 35 | . . . . . . . 8 |
18 | 2, 17 | syl5bi 232 | . . . . . . 7 |
19 | 18 | con1d 139 | . . . . . 6 |
20 | df-nan 1448 | . . . . . . . 8 | |
21 | 20 | biimpri 218 | . . . . . . 7 |
22 | df-nan 1448 | . . . . . . . 8 | |
23 | 22 | biimpri 218 | . . . . . . 7 |
24 | 21, 23 | anim12i 590 | . . . . . 6 |
25 | 19, 24 | syl6 35 | . . . . 5 |
26 | 1, 25 | syl5bi 232 | . . . 4 |
27 | nannan 1451 | . . . 4 | |
28 | nannan 1451 | . . . 4 | |
29 | 26, 27, 28 | 3imtr4i 281 | . . 3 |
30 | 29 | ancli 574 | . 2 |
31 | nannan 1451 | . 2 | |
32 | 30, 31 | mpbir 221 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wo 383 wa 384 wnan 1447 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-nan 1448 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |