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Mirrors > Home > ILE Home > Th. List > necon3ai | Unicode version |
Description: Contrapositive inference for inequality. (Contributed by NM, 23-May-2007.) (Proof rewritten by Jim Kingdon, 15-May-2018.) |
Ref | Expression |
---|---|
necon3ai.1 |
Ref | Expression |
---|---|
necon3ai |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ne 2286 | . 2 | |
2 | necon3ai.1 | . . 3 | |
3 | 2 | con3i 606 | . 2 |
4 | 1, 3 | sylbi 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1316 wne 2285 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-in1 588 ax-in2 589 |
This theorem depends on definitions: df-bi 116 df-ne 2286 |
This theorem is referenced by: disjsn2 3556 0nelxp 4537 fvunsng 5582 map0b 6549 difinfsnlem 6952 hashprg 10522 gcd1 11602 gcdzeq 11637 phimullem 11828 |
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