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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 |
Ref | Expression |
---|---|
necon3ad |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ne 2309 | . 2 | |
2 | necon3ad.1 | . . 3 | |
3 | 2 | con3d 620 | . 2 |
4 | 1, 3 | syl5bi 151 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1331 wne 2308 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-in1 603 ax-in2 604 |
This theorem depends on definitions: df-bi 116 df-ne 2309 |
This theorem is referenced by: necon3d 2352 disjnim 3920 fodjumkvlemres 7033 nlt1pig 7149 eucalglt 11738 nprm 11804 0nnei 12322 |
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