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Axiom ax-1rid 6972
Description: 1 is an identity element for real multiplication. Axiom for real and complex numbers, justified by theorem ax1rid 6932. (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 6869 . . 3 class
31, 2wcel 1393 . 2 wff 𝐴 ∈ ℝ
4 c1 6871 . . . 4 class 1
5 cmul 6875 . . . 4 class ·
61, 4, 5co 5499 . . 3 class (𝐴 · 1)
76, 1wceq 1243 . 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  7005  mulgt1  7805  ltmulgt11  7806  lemulge11  7808  addltmul  8134
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