Theorem remulr

Description: The multiplication operation of the field of reals. (Contributed by Thierry Arnoux, 1-Nov-2017)

	Ref	Expression
Assertion	remulr	⊢ · = ( .r ‘ ℝfld )

Proof

Step	Hyp	Ref	Expression
1		reex	⊢ ℝ ∈ V
2		df-refld	⊢ ℝfld = ( ℂfld ↾s ℝ )
3		cnfldmul	⊢ · = ( .r ‘ ℂfld )
4	2 3	ressmulr	⊢ ( ℝ ∈ V → · = ( .r ‘ ℝfld ) )
5	1 4	ax-mp	⊢ · = ( .r ‘ ℝfld )