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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 |
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neeqtrr.1 |
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neeqtrr.2 |
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Ref | Expression |
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neeqtrri |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neeqtrr.1 |
. 2
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2 | neeqtrr.2 |
. . 3
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3 | 2 | eqcomi 2191 |
. 2
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4 | 1, 3 | neeqtri 2384 |
1
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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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-5 1457 ax-gen 1459 ax-4 1520 ax-17 1536 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-cleq 2180 df-ne 2358 |
This theorem is referenced by: pnfnemnf 8025 basendxnplusgndx 12597 plusgndxnmulrndx 12605 basendxnmulrndx 12606 |
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