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Metamath Proof Explorer

Theorem eqle

Description: Equality implies 'less than or equal to'. (Contributed by NM, 4-Apr-2005)

		Ref	Expression
	Assertion	eqle	$⊢ (A \in ℝ \land A = B) \to A \leq B$

Step	Hyp	Ref	Expression
1		leid	$⊢ A \in ℝ \to A \leq A$
2		breq2	$⊢ A = B \to (A \leq A \leftrightarrow A \leq B)$
3	2	biimpac	$⊢ (A \leq A \land A = B) \to A \leq B$
4	1 3	sylan	$⊢ (A \in ℝ \land A = B) \to A \leq B$