Theorem int-ineqtransd

Description: InequalityTransitivity generator rule. (Contributed by Stanislas Polu, 7-Apr-2020)

	Ref	Expression
Hypotheses	int-ineqtransd.1	$$⊢\phi \to A\in ℝ$$
	int-ineqtransd.2	$$⊢\phi \to B\in ℝ$$
	int-ineqtransd.3	$$⊢\phi \to C\in ℝ$$
	int-ineqtransd.4	$$⊢\phi \to B\le A$$
	int-ineqtransd.5	$$⊢\phi \to C\le B$$
Assertion	int-ineqtransd	$$⊢\phi \to C\le A$$

Proof

Step	Hyp	Ref	Expression
1		int-ineqtransd.1	$$⊢\phi \to A\in ℝ$$
2		int-ineqtransd.2	$$⊢\phi \to B\in ℝ$$
3		int-ineqtransd.3	$$⊢\phi \to C\in ℝ$$
4		int-ineqtransd.4	$$⊢\phi \to B\le A$$
5		int-ineqtransd.5	$$⊢\phi \to C\le B$$
6	3 2 1 5 4	letrd	$$⊢\phi \to C\le A$$