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Mirrors > Home > ILE Home > Th. List > eqnetrd | Unicode version |
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.) |
Ref | Expression |
---|---|
eqnetrd.1 |
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eqnetrd.2 |
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Ref | Expression |
---|---|
eqnetrd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqnetrd.2 |
. 2
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2 | eqnetrd.1 |
. . 3
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3 | 2 | neeq1d 2327 |
. 2
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4 | 1, 3 | mpbird 166 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-5 1424 ax-gen 1426 ax-4 1488 ax-17 1507 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-cleq 2133 df-ne 2310 |
This theorem is referenced by: eqnetrrd 2335 frecabcl 6304 frecsuclem 6311 omp1eomlem 6987 xaddnemnf 9670 xaddnepnf 9671 hashprg 10586 bezoutr1 11757 phibndlem 11928 dfphi2 11932 |
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