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Mirrors > Home > ILE Home > Th. List > ax-1rid | GIF version |
Description: 1 is an identity element for real multiplication. Axiom for real and complex numbers, justified by theorem ax1rid 7709. (Contributed by NM, 29-Jan-1995.) |
Ref | Expression |
---|---|
ax-1rid | ⊢ (𝐴 ∈ ℝ → (𝐴 · 1) = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cr 7643 | . . 3 class ℝ | |
3 | 1, 2 | wcel 1481 | . 2 wff 𝐴 ∈ ℝ |
4 | c1 7645 | . . . 4 class 1 | |
5 | cmul 7649 | . . . 4 class · | |
6 | 1, 4, 5 | co 5782 | . . 3 class (𝐴 · 1) |
7 | 6, 1 | wceq 1332 | . 2 wff (𝐴 · 1) = 𝐴 |
8 | 3, 7 | wi 4 | 1 wff (𝐴 ∈ ℝ → (𝐴 · 1) = 𝐴) |
Colors of variables: wff set class |
This axiom is referenced by: mulid1 7787 mulgt1 8645 ltmulgt11 8646 lemulge11 8648 addltmul 8980 |
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