![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > neeqtrri | Unicode version |
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.) |
Ref | Expression |
---|---|
neeqtrr.1 |
![]() ![]() ![]() ![]() |
neeqtrr.2 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
neeqtrri |
![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neeqtrr.1 |
. 2
![]() ![]() ![]() ![]() | |
2 | neeqtrr.2 |
. . 3
![]() ![]() ![]() ![]() | |
3 | 2 | eqcomi 2119 |
. 2
![]() ![]() ![]() ![]() |
4 | 1, 3 | neeqtri 2309 |
1
![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 586 ax-in2 587 ax-5 1406 ax-gen 1408 ax-4 1470 ax-17 1489 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-cleq 2108 df-ne 2283 |
This theorem is referenced by: pnfnemnf 7744 basendxnplusgndx 11908 plusgndxnmulrndx 11915 basendxnmulrndx 11916 |
Copyright terms: Public domain | W3C validator |