Theorem ssbr

Description: Implication from a subclass relationship of binary relations. (Contributed by Peter Mazsa, 11-Nov-2019)

	Ref	Expression
Assertion	ssbr	⊢ ( 𝐴 ⊆ 𝐵 → ( 𝐶 𝐴 𝐷 → 𝐶 𝐵 𝐷 ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝐴 ⊆ 𝐵 → 𝐴 ⊆ 𝐵 )
2	1	ssbrd	⊢ ( 𝐴 ⊆ 𝐵 → ( 𝐶 𝐴 𝐷 → 𝐶 𝐵 𝐷 ) )