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Axiom ax-1rid 7720
Description: 1 is an identity element for real multiplication. Axiom for real and complex numbers, justified by theorem ax1rid 7678. (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 7612 . . 3 class
31, 2wcel 1480 . 2 wff 𝐴 ∈ ℝ
4 c1 7614 . . . 4 class 1
5 cmul 7618 . . . 4 class ·
61, 4, 5co 5767 . . 3 class (𝐴 · 1)
76, 1wceq 1331 . 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  7756  mulgt1  8614  ltmulgt11  8615  lemulge11  8617  addltmul  8949
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