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Mirrors > Home > ILE Home > Th. List > necon3ad | Unicode version |
Description: Contrapositive law deduction for inequality. (Contributed by NM, 2-Apr-2007.) (Proof rewritten by Jim Kingdon, 15-May-2018.) |
Ref | Expression |
---|---|
necon3ad.1 |
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Ref | Expression |
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necon3ad |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ne 2310 |
. 2
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2 | necon3ad.1 |
. . 3
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3 | 2 | con3d 621 |
. 2
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4 | 1, 3 | syl5bi 151 |
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-ia1 105 ax-in1 604 ax-in2 605 |
This theorem depends on definitions: df-bi 116 df-ne 2310 |
This theorem is referenced by: necon3d 2353 disjnim 3928 fodjumkvlemres 7041 nlt1pig 7173 eucalglt 11774 nprm 11840 0nnei 12361 |
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