![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 2325 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | necon3ai.1 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 2 | con3i 622 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | 1, 3 | sylbi 120 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 2325 |
This theorem is referenced by: disjsn2 3618 0nelxp 4607 fvunsng 5654 map0b 6621 difinfsnlem 7029 hashprg 10659 gcd1 11842 gcdzeq 11877 phimullem 12068 |
Copyright terms: Public domain | W3C validator |