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Mirrors > Home > ILE Home > Th. List > eq2tri | Unicode version |
Description: A compound transitive inference for class equality. (Contributed by NM, 22-Jan-2004.) |
Ref | Expression |
---|---|
eq2tr.1 |
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eq2tr.2 |
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Ref | Expression |
---|---|
eq2tri |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 263 |
. 2
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2 | eq2tr.1 |
. . . 4
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3 | 2 | eqeq2d 2100 |
. . 3
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4 | 3 | pm5.32i 443 |
. 2
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5 | eq2tr.2 |
. . . 4
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6 | 5 | eqeq2d 2100 |
. . 3
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7 | 6 | pm5.32i 443 |
. 2
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8 | 1, 4, 7 | 3bitr3i 209 |
1
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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-5 1382 ax-gen 1384 ax-4 1446 ax-17 1465 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-cleq 2082 |
This theorem is referenced by: xpassen 6602 |
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