ax-xrsvsca - Mathbox for Thierry Arnoux

	Mathbox for Thierry Arnoux		< Previous Next > Nearby theorems
Mirrors > Home > MPE Home > Th. List > Mathboxes > ax-xrsvsca		Structured version Visualization version GIF version

Axiom ax-xrsvsca 32990

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.)

**Assertion**
Ref	Expression
ax-xrsvsca	⊢ ·_e = ( ·_𝑠 ‘ℝ^*_𝑠)

**Detailed syntax breakdown of Axiom ax-xrsvsca**
Step	Hyp	Ref	Expression
1		cxmu 13151	. 2 class ·_e
2		cxrs 17547	. . 3 class ℝ^*_𝑠
3		cvsca 17302	. . 3 class ·_𝑠
4	2, 3	cfv 6563	. 2 class ( ·_𝑠 ‘ℝ^*_𝑠)
5	1, 4	wceq 1537	1 wff ·_e = ( ·_𝑠 ‘ℝ^*_𝑠)

Colors of variables: wff setvar class

This axiom is referenced by: xrge0slmod 33356 sitmcl 34333

W3C validator