Axiom ax-1rid 8286

Description: 1 is an identity element for real multiplication. Axiom for real and complex numbers, justified by Theorem ax1rid 8244. (Contributed by NM, 29-Jan-1995.)

Assertion

Ref	Expression
ax-1rid	⊢ (𝐴 ∈ ℝ → (𝐴 · 1) = 𝐴)

Detailed syntax breakdown of Axiom ax-1rid

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cr 8178	. . 3 class ℝ
3	1, 2	wcel 2209	. 2 wff 𝐴 ∈ ℝ
4		c1 8180	. . . 4 class 1
5		cmul 8184	. . . 4 class ·
6	1, 4, 5	co 6085	. . 3 class (𝐴 · 1)
7	6, 1	wceq 1402	. 2 wff (𝐴 · 1) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℝ → (𝐴 · 1) = 𝐴)

This axiom is used by:  mulrid  8323  mulgt1  9194  ltmulgt11  9195  lemulge11  9197  addltmul  9544