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Mirrors > Home > ILE Home > Th. List > necon2ai | Unicode version |
Description: Contrapositive inference for inequality. (Contributed by NM, 16-Jan-2007.) (Proof rewritten by Jim Kingdon, 16-May-2018.) |
Ref | Expression |
---|---|
necon2ai.1 |
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Ref | Expression |
---|---|
necon2ai |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | necon2ai.1 |
. . 3
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2 | 1 | con2i 617 |
. 2
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3 | df-ne 2310 |
. 2
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4 | 2, 3 | sylibr 133 |
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-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 |
This theorem depends on definitions: df-bi 116 df-ne 2310 |
This theorem is referenced by: necon2i 2365 neneqad 2388 intexr 4083 iin0r 4101 tfrlemisucaccv 6230 pm54.43 7063 renepnf 7837 renemnf 7838 lt0ne0d 8299 nnne0 8772 nn0nepnf 9072 hashennn 10558 bj-intexr 13277 |
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