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Theorem rdglem1 7100
Description: Lemma used with the recursive definition generator. This is a trivial lemma that just changes bound variables for later use. (Contributed by NM, 9-Apr-1995.)
Assertion
Ref Expression
rdglem1
Distinct variable groups:   , , , , ,   , , , ,

Proof of Theorem rdglem1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqid 2457 . . 3
21tfrlem3 7066 . 2
3 fveq2 5871 . . . . . . 7
4 reseq2 5273 . . . . . . . 8
54fveq2d 5875 . . . . . . 7
63, 5eqeq12d 2479 . . . . . 6
76cbvralv 3084 . . . . 5
87anbi2i 694 . . . 4
98rexbii 2959 . . 3
109abbii 2591 . 2
112, 10eqtri 2486 1
Colors of variables: wff setvar class
Syntax hints:  /\wa 369  =wceq 1395  {cab 2442  A.wral 2807  E.wrex 2808   con0 4883  |`cres 5006  Fnwfn 5588  `cfv 5593
This theorem is referenced by:  rdgseg  7107
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
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-ral 2812  df-rex 2813  df-rab 2816  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-uni 4250  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-res 5016  df-iota 5556  df-fun 5595  df-fn 5596  df-fv 5601
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