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Mirrors > Home > ILE Home > Th. List > 3eqtrri | Unicode version |
Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
3eqtri.1 |
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3eqtri.2 |
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3eqtri.3 |
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Ref | Expression |
---|---|
3eqtrri |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eqtri.1 |
. . 3
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2 | 3eqtri.2 |
. . 3
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3 | 1, 2 | eqtri 2115 |
. 2
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4 | 3eqtri.3 |
. 2
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5 | 3, 4 | eqtr2i 2116 |
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 1388 ax-gen 1390 ax-4 1452 ax-17 1471 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-cleq 2088 |
This theorem is referenced by: resindm 4787 dfdm2 4999 cofunex2g 5921 df1st2 6022 df2nd2 6023 enq0enq 7087 dfn2 8784 9p1e10 8978 0.999... 11064 |
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