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Mirrors > Home > ILE Home > Th. List > con4biddc | Unicode version |
Description: A contraposition deduction. (Contributed by Jim Kingdon, 18-May-2018.) |
Ref | Expression |
---|---|
con4biddc.1 | DECID DECID |
Ref | Expression |
---|---|
con4biddc | DECID DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con4biddc.1 | . . . . . 6 DECID DECID | |
2 | biimpr 129 | . . . . . 6 | |
3 | 1, 2 | syl8 71 | . . . . 5 DECID DECID |
4 | condc 839 | . . . . . 6 DECID | |
5 | 4 | a2i 11 | . . . . 5 DECID DECID |
6 | 3, 5 | syl6 33 | . . . 4 DECID DECID |
7 | 6 | imp31 254 | . . 3 DECID DECID |
8 | biimp 117 | . . . . . 6 | |
9 | 1, 8 | syl8 71 | . . . . 5 DECID DECID |
10 | condc 839 | . . . . . 6 DECID | |
11 | 10 | imim2d 54 | . . . . 5 DECID DECID DECID |
12 | 9, 11 | sylcom 28 | . . . 4 DECID DECID |
13 | 12 | imp31 254 | . . 3 DECID DECID |
14 | 7, 13 | impbid 128 | . 2 DECID DECID |
15 | 14 | exp31 362 | 1 DECID DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 DECID wdc 820 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 |
This theorem depends on definitions: df-bi 116 df-stab 817 df-dc 821 |
This theorem is referenced by: necon4abiddc 2400 |
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