Theorem brresi2 38391

Description: Restriction of a binary relation. (Contributed by Jeff Madsen, 2-Sep-2009.)

Hypothesis

Ref	Expression
brresi2.1	⊢ 𝐵 ∈ V

Assertion

Ref	Expression
brresi2	⊢ (𝐴(𝑅 ↾ 𝐶)𝐵 → 𝐴𝑅𝐵)

Proof of Theorem brresi2

Step	Hyp	Ref	Expression
1		resss 6000	. 2 ⊢ (𝑅 ↾ 𝐶) ⊆ 𝑅
2	1	ssbri 5156	1 ⊢ (𝐴(𝑅 ↾ 𝐶)𝐵 → 𝐴𝑅𝐵)

Syntax hints:   → wi 4   ∈ wcel 2143  Vcvv 3455   class class class wbr 5109   ↾ cres 5663

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-in 3912  df-ss 3922  df-br 5110  df-res 5673

This theorem is referenced by: (None)