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Mirrors > Home > ILE Home > Th. List > neeqtri | Unicode version |
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.) |
Ref | Expression |
---|---|
neeqtr.1 | |
neeqtr.2 |
Ref | Expression |
---|---|
neeqtri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neeqtr.1 | . 2 | |
2 | neeqtr.2 | . . 3 | |
3 | 2 | neeq2i 2343 | . 2 |
4 | 1, 3 | mpbi 144 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1335 wne 2327 |
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 ax-5 1427 ax-gen 1429 ax-4 1490 ax-17 1506 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-cleq 2150 df-ne 2328 |
This theorem is referenced by: neeqtrri 2356 |
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