Theorem ssbri

Description: Inference from a subclass relationship of binary relations. (Contributed by NM, 28-Mar-2007) (Revised by Mario Carneiro, 8-Feb-2015)

	Ref	Expression
Hypothesis	ssbri.1	⊢ 𝐴 ⊆ 𝐵
Assertion	ssbri	⊢ ( 𝐶 𝐴 𝐷 → 𝐶 𝐵 𝐷 )

Proof

Step	Hyp	Ref	Expression
1		ssbri.1	⊢ 𝐴 ⊆ 𝐵
2		ssbr	⊢ ( 𝐴 ⊆ 𝐵 → ( 𝐶 𝐴 𝐷 → 𝐶 𝐵 𝐷 ) )
3	1 2	ax-mp	⊢ ( 𝐶 𝐴 𝐷 → 𝐶 𝐵 𝐷 )