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

Metamath Proof Explorer

Theorem rexaddd

Description: The extended real addition operation when both arguments are real. Deduction version of rexadd . (Contributed by Glauco Siliprandi, 24-Dec-2020)

	Ref	Expression
Hypotheses	rexaddd.1	$⊢ φ \to A \in ℝ$
	rexaddd.2	$⊢ φ \to B \in ℝ$
Assertion	rexaddd	$⊢ φ \to A +_{𝑒} B = A + B$

Proof

Step	Hyp	Ref	Expression
1		rexaddd.1	$⊢ φ \to A \in ℝ$
2		rexaddd.2	$⊢ φ \to B \in ℝ$
3		rexadd	$⊢ (A \in ℝ \land B \in ℝ) \to A +_{𝑒} B = A + B$
4	1 2 3	syl2anc	$⊢ φ \to A +_{𝑒} B = A + B$