![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 6761. (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 6710 | . . 3 class ℝ | |
3 | 1, 2 | wcel 1390 | . 2 wff A ∈ ℝ |
4 | c1 6712 | . . . 4 class 1 | |
5 | cmul 6716 | . . . 4 class · | |
6 | 1, 4, 5 | co 5455 | . . 3 class (A · 1) |
7 | 6, 1 | wceq 1242 | . 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 6822 mulgt1 7610 ltmulgt11 7611 lemulge11 7613 addltmul 7938 |
Copyright terms: Public domain | W3C validator |