Theorem ssbr 5117

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 5116	1 ⊢ (𝐴 ⊆ 𝐵 → (𝐶𝐴𝐷 → 𝐶𝐵𝐷))

Syntax hints:   → wi 4   ⊆ wss 3883   class class class wbr 5073

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787  df-clel 2814  df-ss 3900  df-br 5074

This theorem is referenced by:  ssbri  5118  coss1  5798  coss2  5799  cnvss  5815  ssrelrn  5837  ttrclss  9633  chnrss  18573  isucn2  24262  brelg  32700  cossss  38891