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Theorem eqrelriiv 5102
Description: Inference from extensionality principle for relations. (Contributed by NM, 17-Mar-1995.)
Hypotheses
Ref Expression
eqreliiv.1
eqreliiv.2
eqreliiv.3
Assertion
Ref Expression
eqrelriiv
Distinct variable groups:   , ,   , ,

Proof of Theorem eqrelriiv
StepHypRef Expression
1 eqreliiv.1 . 2
2 eqreliiv.2 . 2
3 eqreliiv.3 . . 3
43eqrelriv 5101 . 2
51, 2, 4mp2an 672 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  =wceq 1395  e.wcel 1818  <.cop 4035  Relwrel 5009
This theorem is referenced by:  eqbrriv  5103  inopab  5138  difopab  5139  dfres2  5331  restidsing  5335  cnvopab  5412  cnv0  5414  cnvdif  5417  difxp  5436  cnvcnvsn  5490  dfco2  5511  coiun  5522  co02  5526  coass  5531  ressn  5548  ovoliunlem1  21913  h2hlm  25897  cnvco1  29189  cnvco2  29190
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-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
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