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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 | |
3eqtri.2 | |
3eqtri.3 |
Ref | Expression |
---|---|
3eqtrri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eqtri.1 | . . 3 | |
2 | 3eqtri.2 | . . 3 | |
3 | 1, 2 | eqtri 2178 | . 2 |
4 | 3eqtri.3 | . 2 | |
5 | 3, 4 | eqtr2i 2179 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1335 |
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-5 1427 ax-gen 1429 ax-4 1490 ax-17 1506 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-cleq 2150 |
This theorem is referenced by: resindm 4907 dfdm2 5119 cofunex2g 6057 df1st2 6163 df2nd2 6164 enq0enq 7346 dfn2 9098 9p1e10 9292 0.999... 11413 sincosq3sgn 13136 sincosq4sgn 13137 |
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