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Theorem isexid 21910
 Description: The predicate has a left and right identity element. (Contributed by FL, 2-Nov-2009.) (Revised by Mario Carneiro, 22-Dec-2013.) (New usage is discouraged.)
Hypothesis
Ref Expression
isexid.1
Assertion
Ref Expression
isexid
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem isexid
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dmeq 5073 . . . . 5
21dmeqd 5075 . . . 4
3 isexid.1 . . . 4
42, 3syl6eqr 2488 . . 3
5 oveq 6090 . . . . . 6
65eqeq1d 2446 . . . . 5
7 oveq 6090 . . . . . 6
87eqeq1d 2446 . . . . 5
96, 8anbi12d 693 . . . 4
104, 9raleqbidv 2918 . . 3
114, 10rexeqbidv 2919 . 2
12 df-exid 21908 . 2
1311, 12elab2g 3086 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  wral 2707  wrex 2708   cdm 4881  (class class class)co 6084   cexid 21907 This theorem is referenced by:  opidon  21915  isexid2  21918  ismndo  21936  exidres  26567 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-dm 4891  df-iota 5421  df-fv 5465  df-ov 6087  df-exid 21908
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