Theorem brresi2 38220

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 5988	. 2 ⊢ (𝑅 ↾ 𝐶) ⊆ 𝑅
2	1	ssbri 5146	1 ⊢ (𝐴(𝑅 ↾ 𝐶)𝐵 → 𝐴𝑅𝐵)

Syntax hints:   → wi 4   ∈ wcel 2143  Vcvv 3455   class class class wbr 5101   ↾ cres 5650

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1816  ax-4 1830  ax-5 1931  ax-6 1988  ax-7 2029  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1564  df-ex 1801  df-sb 2092  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-in 3912  df-ss 3922  df-br 5102  df-res 5660

This theorem is referenced by: (None)