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Mirrors > Home > ILE Home > Th. List > 3eqtr2ri | 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 |
---|---|
3eqtr2i.1 | |
3eqtr2i.2 | |
3eqtr2i.3 |
Ref | Expression |
---|---|
3eqtr2ri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eqtr2i.1 | . . 3 | |
2 | 3eqtr2i.2 | . . 3 | |
3 | 1, 2 | eqtr4i 2104 | . 2 |
4 | 3eqtr2i.3 | . 2 | |
5 | 3, 4 | eqtr2i 2102 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1284 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-4 1440 ax-17 1459 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-cleq 2074 |
This theorem is referenced by: funimacnv 4995 uniqs 6187 |
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