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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 |
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Ref | Expression |
---|---|
con2d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con2d.1 |
. . . 4
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2 | ax-in2 615 |
. . . 4
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3 | 1, 2 | syl6 33 |
. . 3
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4 | 3 | com23 78 |
. 2
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5 | pm2.01 616 |
. 2
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6 | 4, 5 | syl6 33 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-in1 614 ax-in2 615 |
This theorem is referenced by: mt2d 625 con3d 631 pm3.2im 637 con2 643 pm2.65 659 con1biimdc 873 exists2 2123 necon2ad 2404 necon2bd 2405 minel 3485 nlimsucg 4566 poirr2 5022 funun 5261 imadif 5297 infnlbti 7025 mkvprop 7156 addnidpig 7335 zltnle 9299 zdcle 9329 btwnnz 9347 prime 9352 icc0r 9926 fznlem 10041 qltnle 10246 bcval4 10732 seq3coll 10822 fsum3cvg 11386 fsumsplit 11415 fproddccvg 11580 fprodsplitdc 11604 2sqpwodd 12176 pockthg 12355 prmunb 12360 logbgcd1irr 14388 lgsne0 14442 |
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