Theorem disjALTVidres 38152

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 38151	. 2 ⊢ Disj I
2		disjimres 38146	. 2 ⊢ ( Disj I → Disj ( I ↾ 𝐴))
3	1, 2	ax-mp 5	1 ⊢ Disj ( I ↾ 𝐴)

Syntax hints:   I cid 5569   ↾ cres 5674   Disj wdisjALTV 37604

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2164  ax-ext 2698  ax-sep 5293  ax-nul 5300  ax-pr 5423

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-ral 3057  df-rex 3066  df-rab 3428  df-v 3471  df-dif 3947  df-un 3949  df-in 3951  df-ss 3961  df-nul 4319  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-br 5143  df-opab 5205  df-id 5570  df-xp 5678  df-rel 5679  df-cnv 5680  df-co 5681  df-dm 5682  df-rn 5683  df-res 5684  df-coss 37807  df-cnvrefrel 37923  df-funALTV 38078  df-disjALTV 38101

This theorem is referenced by:  eqvrel1cossidres  38186  detidres  38191  petidres2  38214