Axiom ax-1rid 8199

Description: 1 is an identity element for real multiplication. Axiom for real and complex numbers, justified by Theorem ax1rid 8157. (Contributed by NM, 29-Jan-1995.)

Assertion

Ref	Expression
ax-1rid	|- ( A e. RR -> ( A x. 1 ) = A )

Detailed syntax breakdown of Axiom ax-1rid

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cr 8091	. . 3 class RR
3	1, 2	wcel 2202	. 2 wff A e. RR
4		c1 8093	. . . 4 class 1
5		cmul 8097	. . . 4 class x.
6	1, 4, 5	co 6028	. . 3 class ( A x. 1 )
7	6, 1	wceq 1398	. 2 wff ( A x. 1 ) = A
8	3, 7	wi 4	1 wff ( A e. RR -> ( A x. 1 ) = A )

This axiom is referenced by:  mulrid  8236  mulgt1  9102  ltmulgt11  9103  lemulge11  9105  addltmul  9440