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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ax-xrsvsca | Structured version Visualization version GIF version |
Description: Assume the scalar product of the extended real structure is the extended real number multiplication operation (this has to be defined in the main body of set.mm). (Contributed by Thierry Arnoux, 22-Oct-2017.) |
Ref | Expression |
---|---|
ax-xrsvsca | ⊢ ·e = ( ·𝑠 ‘ℝ*𝑠) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cxmu 12232 | . 2 class ·e | |
2 | cxrs 16514 | . . 3 class ℝ*𝑠 | |
3 | cvsca 16310 | . . 3 class ·𝑠 | |
4 | 2, 3 | cfv 6124 | . 2 class ( ·𝑠 ‘ℝ*𝑠) |
5 | 1, 4 | wceq 1658 | 1 wff ·e = ( ·𝑠 ‘ℝ*𝑠) |
Colors of variables: wff setvar class |
This axiom is referenced by: xrge0slmod 30390 sitmcl 30959 |
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