This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem resubid1

Description: Real number version of subid1 without ax-mulcom . (Contributed by SN, 23-Jan-2024)

		Ref	Expression
	Assertion	resubid1	$⊢ A \in ℝ \to A -_{ℝ} 0 = A$

Step	Hyp	Ref	Expression
1		readdlid	$⊢ A \in ℝ \to 0 + A = A$
2		id	$⊢ A \in ℝ \to A \in ℝ$
3		elre0re	$⊢ A \in ℝ \to 0 \in ℝ$
4	2 3 2	resubaddd	$⊢ A \in ℝ \to (A -_{ℝ} 0 = A \leftrightarrow 0 + A = A)$
5	1 4	mpbird	$⊢ A \in ℝ \to A -_{ℝ} 0 = A$