![]() |
Higher-Order Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > HOLE Home > Th. List > pm2.21 | Unicode version |
Description: A falsehood implies anything. (Contributed by Mario Carneiro, 9-Oct-2014.) |
Ref | Expression |
---|---|
pm2.21.1 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
pm2.21 |
![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wfal 135 |
. . . 4
![]() ![]() ![]() ![]() | |
2 | 1 | id 25 |
. . 3
![]() ![]() ![]() ![]() |
3 | df-fal 127 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 1, 3 | a1i 28 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 2, 4 | mpbi 82 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | wv 64 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() | |
7 | pm2.21.1 |
. . 3
![]() ![]() ![]() ![]() | |
8 | 6, 7 | weqi 76 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | 8 | id 25 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 6, 7, 9 | cla4v 152 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | 5, 10 | syl 16 |
1
![]() ![]() ![]() ![]() |
Colors of variables: type var term |
Syntax hints: tv 1
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-simpl 20 ax-simpr 21 ax-id 24 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-wctl 31 ax-wctr 32 ax-weq 40 ax-refl 42 ax-eqmp 45 ax-ded 46 ax-wct 47 ax-wc 49 ax-ceq 51 ax-wv 63 ax-wl 65 ax-beta 67 ax-distrc 68 ax-leq 69 ax-wov 71 ax-eqtypi 77 ax-eqtypri 80 ax-hbl1 103 ax-17 105 ax-inst 113 |
This theorem depends on definitions: df-ov 73 df-al 126 df-fal 127 |
This theorem is referenced by: notval2 159 notnot 200 ax3 205 |
Copyright terms: Public domain | W3C validator |