Theorem releqi 3244

Description: Equality inference for the relation predicate.

Hypothesis

Ref	Expression
releqi.1	|- A = B

Assertion

Ref	Expression
releqi	|- (Rel A <-> Rel B)

Proof of Theorem releqi

Step	Hyp	Ref	Expression
1		releqi.1	. 2 |- A = B
2		releq 3243	. 2 |- (A = B -> (Rel A <-> Rel B))
3	1, 2	ax-mp 7	1 |- (Rel A <-> Rel B)

Syntax hints:   <-> wb 146   = wceq 956  Rel wrel 3175

This theorem is referenced by:  reli 3273  rele 3274  relcnv 3435  relco 3484  reloprab 3992  reldmoprab 4005  ndmoprcl 4044  mapsspw 4341  relen 4372  reldom 4373  relsdom 4374  mapdom2lem 4493  aceq3lem 4732  ndmioo 6370  elfzlem 6473  climrel 6976  eltopsp 7604  tpsex 7605  msrel 7797  isring 8141  vcrel 8166  hmeogrp 10538  hgrarel 10768

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-in 2051  df-ss 2053  df-rel 3185

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