Theorem resabs1d 5308

Description: Absorption law for restriction, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019.)

Hypothesis

Ref	Expression
resabs1d.b

Assertion

Ref	Expression
resabs1d

Proof of Theorem resabs1d

Step	Hyp	Ref	Expression
1		resabs1d.b	. 2
2		resabs1 5307	. 2
3	1, 2	syl 16	1

Syntax hints:  ->wi 4  =wceq 1395  C_wss 3475  |`cres 5006

This theorem is referenced by:  f2ndf  6906  ablfac1eulem  17123  kgencn2  20058  tsmsres  20646  resubmet  21307  xrge0gsumle  21338  cmsss  21789  minveclem3a  21842  dvlip2  22396  c1liplem1  22397  efcvx  22844  logccv  23044  loglesqrt  23132  wilthlem2  23343  cvmlift2lem9  28756  mbfresfi  30061  ssbnd  30284  prdsbnd2  30291  cnpwstotbnd  30293  reheibor  30335  diophin  30706  fnwe2lem2  30997  dvsid  31236  limcresiooub  31648  limcresioolb  31649  dvmptresicc  31716  fourierdlem46  31935  fourierdlem48  31937  fourierdlem49  31938  fourierdlem58  31947  fourierdlem72  31961  fourierdlem73  31962  fourierdlem74  31963  fourierdlem75  31964  fourierdlem89  31978  fourierdlem90  31979  fourierdlem91  31980  fourierdlem93  31982  fourierdlem100  31989  fourierdlem102  31991  fourierdlem103  31992  fourierdlem104  31993  fourierdlem107  31996  fourierdlem111  32000  fourierdlem112  32001  fourierdlem114  32003  afvres  32257  funcrngcsetc  32806  funcrngcsetcALT  32807  funcringcsetc  32843  bnj1280  34076

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-xp 5010  df-rel 5011  df-res 5016