Theorem brresi2 35804

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 5905	. 2 ⊢ (𝑅 ↾ 𝐶) ⊆ 𝑅
2	1	ssbri 5115	1 ⊢ (𝐴(𝑅 ↾ 𝐶)𝐵 → 𝐴𝑅𝐵)

Syntax hints:   → wi 4   ∈ wcel 2108  Vcvv 3422   class class class wbr 5070   ↾ cres 5582

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-br 5071  df-res 5592

This theorem is referenced by: (None)