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Theorem relinxp 34391
 Description: Intersection with a Cartesian product is a relation. (Contributed by Peter Mazsa, 4-Mar-2019.)
Assertion
Ref Expression
relinxp Rel (𝑅 ∩ (𝐴 × 𝐵))

Proof of Theorem relinxp
StepHypRef Expression
1 relxp 5281 . 2 Rel (𝐴 × 𝐵)
2 relin2 5391 . 2 (Rel (𝐴 × 𝐵) → Rel (𝑅 ∩ (𝐴 × 𝐵)))
31, 2ax-mp 5 1 Rel (𝑅 ∩ (𝐴 × 𝐵))
 Colors of variables: wff setvar class Syntax hints:   ∩ cin 3712   × cxp 5262  Rel wrel 5269 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1986  ax-6 2052  ax-7 2088  ax-9 2146  ax-10 2166  ax-11 2181  ax-12 2194  ax-13 2389  ax-ext 2738 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2045  df-clab 2745  df-cleq 2751  df-clel 2754  df-nfc 2889  df-v 3340  df-in 3720  df-ss 3727  df-opab 4863  df-xp 5270  df-rel 5271 This theorem is referenced by:  inxpss  34404  inxpss2  34407  iss2  34433  inxp2  34450  inxpxrn  34474
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