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Mirrors > Home > ILE Home > Th. List > con2d | Unicode version |
Description: A contraposition deduction. (Contributed by NM, 19-Aug-1993.) (Revised by NM, 12-Feb-2013.) |
Ref | Expression |
---|---|
con2d.1 |
Ref | Expression |
---|---|
con2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con2d.1 | . . . 4 | |
2 | ax-in2 604 | . . . 4 | |
3 | 1, 2 | syl6 33 | . . 3 |
4 | 3 | com23 78 | . 2 |
5 | pm2.01 605 | . 2 | |
6 | 4, 5 | syl6 33 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-in1 603 ax-in2 604 |
This theorem is referenced by: mt2d 614 con3d 620 pm3.2im 626 con2 632 pm2.65 648 con1biimdc 858 exists2 2096 necon2ad 2365 necon2bd 2366 minel 3424 nlimsucg 4481 poirr2 4931 funun 5167 imadif 5203 infnlbti 6913 mkvprop 7032 addnidpig 7147 zltnle 9103 zdcle 9130 btwnnz 9148 prime 9153 icc0r 9712 fznlem 9824 qltnle 10026 bcval4 10501 seq3coll 10588 fsum3cvg 11150 fsumsplit 11179 fproddccvg 11344 2sqpwodd 11857 |
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