Theorem disjimres 39388

Description: Disjointness condition for restriction. (Contributed by Peter Mazsa, 27-Sep-2021.)

Assertion

Ref	Expression
disjimres	⊢ ( Disj 𝑅 → Disj (𝑅 ↾ 𝐴))

Proof of Theorem disjimres

Step	Hyp	Ref	Expression
1		resss 6001	. 2 ⊢ (𝑅 ↾ 𝐴) ⊆ 𝑅
2	1	disjssi 39370	1 ⊢ ( Disj 𝑅 → Disj (𝑅 ↾ 𝐴))

Syntax hints:   → wi 4   ↾ cres 5664   Disj wdisjALTV 38757

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-11 2198  ax-ext 2741  ax-sep 5261  ax-pr 5405

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1103  df-tru 1570  df-fal 1580  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-ral 3086  df-rex 3096  df-rab 3424  df-v 3465  df-dif 3916  df-un 3918  df-in 3920  df-ss 3930  df-nul 4295  df-if 4493  df-sn 4595  df-pr 4597  df-op 4601  df-br 5114  df-opab 5178  df-id 5557  df-xp 5668  df-rel 5669  df-cnv 5670  df-co 5671  df-dm 5672  df-rn 5673  df-res 5674  df-coss 39039  df-cnvrefrel 39145  df-funALTV 39305  df-disjALTV 39328

This theorem is referenced by:  disjiminres  39390  disjimxrnres  39391  disjALTVidres  39394