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Axiom ax-1rid 7506
Description: 1 is an identity element for real multiplication. Axiom for real and complex numbers, justified by theorem ax1rid 7466. (Contributed by NM, 29-Jan-1995.)
Assertion
Ref Expression
ax-1rid (𝐴 ∈ ℝ → (𝐴 · 1) = 𝐴)

Detailed syntax breakdown of Axiom ax-1rid
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cr 7403 . . 3 class
31, 2wcel 1439 . 2 wff 𝐴 ∈ ℝ
4 c1 7405 . . . 4 class 1
5 cmul 7409 . . . 4 class ·
61, 4, 5co 5666 . . 3 class (𝐴 · 1)
76, 1wceq 1290 . 2 wff (𝐴 · 1) = 𝐴
83, 7wi 4 1 wff (𝐴 ∈ ℝ → (𝐴 · 1) = 𝐴)
Colors of variables: wff set class
This axiom is referenced by:  mulid1  7539  mulgt1  8378  ltmulgt11  8379  lemulge11  8381  addltmul  8706
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