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Mirrors > Home > ILE Home > Th. List > eqnetri | Unicode version |
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.) |
Ref | Expression |
---|---|
eqnetr.1 | |
eqnetr.2 |
Ref | Expression |
---|---|
eqnetri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqnetr.2 | . 2 | |
2 | eqnetr.1 | . . 3 | |
3 | 2 | neeq1i 2323 | . 2 |
4 | 1, 3 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 wne 2308 |
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 603 ax-in2 604 ax-5 1423 ax-gen 1425 ax-4 1487 ax-17 1506 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-cleq 2132 df-ne 2309 |
This theorem is referenced by: eqnetrri 2333 2on0 6323 1n0 6329 basendxnplusgndx 12065 plusgndxnmulrndx 12072 basendxnmulrndx 12073 |
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