Theorem xmulid2

Description: Extended real version of mulid2 . (Contributed by Mario Carneiro, 20-Aug-2015)

	Ref	Expression
Assertion	xmulid2	⊢ ( 𝐴 ∈ ℝ* → ( 1 ·e 𝐴 ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		1xr	⊢ 1 ∈ ℝ*
2		xmulcom	⊢ ( ( 1 ∈ ℝ* ∧ 𝐴 ∈ ℝ* ) → ( 1 ·e 𝐴 ) = ( 𝐴 ·e 1 ) )
3	1 2	mpan	⊢ ( 𝐴 ∈ ℝ* → ( 1 ·e 𝐴 ) = ( 𝐴 ·e 1 ) )
4		xmulid1	⊢ ( 𝐴 ∈ ℝ* → ( 𝐴 ·e 1 ) = 𝐴 )
5	3 4	eqtrd	⊢ ( 𝐴 ∈ ℝ* → ( 1 ·e 𝐴 ) = 𝐴 )