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Metamath Proof Explorer

Theorem readdrid

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

		Ref	Expression
	Assertion	readdrid	$⊢ A \in ℝ \to A + 0 = A$

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