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Theorem nmzbi 14985
 Description: Defining property of the normalizer. (Contributed by Mario Carneiro, 18-Jan-2015.)
Hypothesis
Ref Expression
elnmz.1
Assertion
Ref Expression
nmzbi
Distinct variable groups:   ,   ,,   , ,   ,,
Allowed substitution hints:   ()   (,)   (,)

Proof of Theorem nmzbi
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elnmz.1 . . . 4
21elnmz 14984 . . 3
32simprbi 452 . 2
4 oveq2 6092 . . . . 5
54eleq1d 2504 . . . 4
6 oveq1 6091 . . . . 5
76eleq1d 2504 . . . 4
85, 7bibi12d 314 . . 3
98rspccva 3053 . 2
103, 9sylan 459 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  wral 2707  crab 2711  (class class class)co 6084 This theorem is referenced by:  nmzsubg  14986  nmznsg  14989  conjnmz  15044 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-iota 5421  df-fv 5465  df-ov 6087
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