Axiom ax-1rid 8144

Description: 1 is an identity element for real multiplication. Axiom for real and complex numbers, justified by Theorem ax1rid 8102. (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 8036	. . 3 class ℝ
3	1, 2	wcel 2201	. 2 wff 𝐴 ∈ ℝ
4		c1 8038	. . . 4 class 1
5		cmul 8042	. . . 4 class ·
6	1, 4, 5	co 6023	. . 3 class (𝐴 · 1)
7	6, 1	wceq 1397	. 2 wff (𝐴 · 1) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℝ → (𝐴 · 1) = 𝐴)

This axiom is referenced by:  mulrid  8181  mulgt1  9048  ltmulgt11  9049  lemulge11  9051  addltmul  9386