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Mirrors > Home > NFE Home > Th. List > 3eqtr3d | Unicode version |
Description: A deduction from three chained equalities. (Contributed by NM, 4-Aug-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
3eqtr3d.1 | |
3eqtr3d.2 | |
3eqtr3d.3 |
Ref | Expression |
---|---|
3eqtr3d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eqtr3d.1 | . . 3 | |
2 | 3eqtr3d.2 | . . 3 | |
3 | 1, 2 | eqtr3d 2387 | . 2 |
4 | 3eqtr3d.3 | . 2 | |
5 | 3, 4 | eqtr3d 2387 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-ex 1542 df-cleq 2346 |
This theorem is referenced by: nnsucelr 4428 f1ocnvfv1 5476 enadj 6060 ncdisjun 6136 |
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