Theorem ssbr 5133

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

Assertion

Ref	Expression
ssbr	⊢ (𝐴 ⊆ 𝐵 → (𝐶𝐴𝐷 → 𝐶𝐵𝐷))

Proof of Theorem ssbr

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝐴 ⊆ 𝐵 → 𝐴 ⊆ 𝐵)
2	1	ssbrd 5132	1 ⊢ (𝐴 ⊆ 𝐵 → (𝐶𝐴𝐷 → 𝐶𝐵𝐷))

Syntax hints:   → wi 4   ⊆ wss 3897   class class class wbr 5089

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781  df-clel 2806  df-ss 3914  df-br 5090

This theorem is referenced by:  ssbri  5134  coss1  5794  coss2  5795  cnvss  5811  ssrelrn  5833  ttrclss  9610  chnrss  18521  isucn2  24193  brelg  32590  cossss  38537