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Theorem difeq2i 3703
Description: Inference adding difference to the left in a class equality. (Contributed by NM, 15-Nov-2002.)
Hypothesis
Ref Expression
difeq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
difeq2i (𝐶𝐴) = (𝐶𝐵)

Proof of Theorem difeq2i
StepHypRef Expression
1 difeq1i.1 . 2 𝐴 = 𝐵
2 difeq2 3700 . 2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
31, 2ax-mp 5 1 (𝐶𝐴) = (𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  cdif 3552
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-ral 2912  df-rab 2916  df-dif 3558
This theorem is referenced by:  difeq12i  3704  dfun3  3841  dfin3  3842  dfin4  3843  invdif  3844  indif  3845  difundi  3855  difindi  3857  difdif2  3860  dif32  3867  difabs  3868  dfsymdif3  3869  notrab  3880  dif0  3924  unvdif  4014  difdifdir  4028  dfif3  4072  difpr  4303  iinvdif  4558  cnvin  5499  fndifnfp  6396  dif1o  7525  dfsdom2  8027  cda1dif  8942  m1bits  15086  clsval2  20764  mretopd  20806  cmpfi  21121  llycmpkgen2  21263  pserdvlem2  24086  nbgrssvwo2  26148  clwwlknclwwlkdifs  26740  frgrregorufr0  27047  iundifdifd  29225  iundifdif  29226  difres  29258  sibfof  30183  eulerpartlemmf  30218  kur14lem2  30897  kur14lem6  30901  kur14lem7  30902  dfon4  31642  onint1  32090  bj-2upln1upl  32659  poimirlem8  33049  diophren  36857  nonrel  37371  dssmapntrcls  37908  salincl  39850  meaiuninc  40005  carageniuncllem1  40042
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