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Mirrors > Home > HOLE Home > Th. List > con2d | Unicode version |
Description: A contraposition deduction. |
Ref | Expression |
---|---|
con2d.1 | |
con2d.2 |
Ref | Expression |
---|---|
con2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con2d.1 | . . . . 5 | |
2 | wfal 125 | . . . . 5 | |
3 | con2d.2 | . . . . . 6 | |
4 | 3 | ax-cb1 29 | . . . . . . 7 |
5 | 1 | notval 135 | . . . . . . 7 |
6 | 4, 5 | a1i 28 | . . . . . 6 |
7 | 3, 6 | mpbi 72 | . . . . 5 |
8 | 1, 2, 7 | imp 147 | . . . 4 |
9 | 8 | an32s 55 | . . 3 |
10 | 9 | ex 148 | . 2 |
11 | 4 | wctl 31 | . . . 4 |
12 | 11, 1 | wct 44 | . . 3 |
13 | 4 | wctr 32 | . . . 4 |
14 | 13 | notval 135 | . . 3 |
15 | 12, 14 | a1i 28 | . 2 |
16 | 10, 15 | mpbir 77 | 1 |
Colors of variables: type var term |
Syntax hints: hb 3 kc 5 ke 7 kbr 9 kct 10 wffMMJ2 11 wffMMJ2t 12 tfal 108 tne 110 tim 111 |
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-refl 39 ax-eqmp 42 ax-ded 43 ax-ceq 46 ax-beta 60 ax-distrc 61 ax-leq 62 ax-distrl 63 ax-hbl1 93 ax-17 95 ax-inst 103 |
This theorem depends on definitions: df-ov 65 df-al 116 df-fal 117 df-an 118 df-im 119 df-not 120 |
This theorem is referenced by: con3d 152 exnal1 175 |
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