Theorem disjALTVidres 38741

Description: The class of identity relations restricted is disjoint. (Contributed by Peter Mazsa, 28-Jun-2020.) (Revised by Peter Mazsa, 27-Sep-2021.)

Assertion

Ref	Expression
disjALTVidres	⊢ Disj ( I ↾ 𝐴)

Proof of Theorem disjALTVidres

Step	Hyp	Ref	Expression
1		disjALTVid 38740	. 2 ⊢ Disj I
2		disjimres 38735	. 2 ⊢ ( Disj I → Disj ( I ↾ 𝐴))
3	1, 2	ax-mp 5	1 ⊢ Disj ( I ↾ 𝐴)

Syntax hints:   I cid 5525   ↾ cres 5633   Disj wdisjALTV 38196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-10 2142  ax-11 2158  ax-12 2178  ax-ext 2701  ax-sep 5246  ax-nul 5256  ax-pr 5382

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-ral 3045  df-rex 3054  df-rab 3403  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4293  df-if 4485  df-sn 4586  df-pr 4588  df-op 4592  df-br 5103  df-opab 5165  df-id 5526  df-xp 5637  df-rel 5638  df-cnv 5639  df-co 5640  df-dm 5641  df-rn 5642  df-res 5643  df-coss 38395  df-cnvrefrel 38511  df-funALTV 38667  df-disjALTV 38690

This theorem is referenced by:  eqvrel1cossidres  38775  detidres  38780  petidres2  38803