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Theorem eqrel 5097
Description: Extensionality principle for relations. Theorem 3.2(ii) of [Monk1] p. 33. (Contributed by NM, 2-Aug-1994.)
Assertion
Ref Expression
eqrel
Distinct variable groups:   , ,   , ,

Proof of Theorem eqrel
StepHypRef Expression
1 ssrel 5096 . . 3
2 ssrel 5096 . . 3
31, 2bi2anan9 873 . 2
4 eqss 3518 . 2
5 2albiim 1700 . 2
63, 4, 53bitr4g 288 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  C_wss 3475  <.cop 4035  Relwrel 5009
This theorem is referenced by:  eqrelriv  5101  eqrelrdv  5104  eqbrrdv  5105  eqrelrdv2  5107  opabid2  5137  reldm0  5225  iss  5326  asymref  5388  funssres  5633  fsn  6069
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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