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Theorem frrlem3 28966
 Description: Lemma for founded recursion. An acceptable function's domain is a subset of . (Contributed by Paul Chapman, 21-Apr-2012.)
Hypothesis
Ref Expression
frrlem1.1
Assertion
Ref Expression
frrlem3
Distinct variable groups:   ,,,,   ,,,,   ,,,,
Allowed substitution hints:   (,,,)

Proof of Theorem frrlem3
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 frrlem1.1 . . . 4
21frrlem1 28964 . . 3
32abeq2i 2594 . 2
4 fndm 5678 . . . 4
5 simp1 996 . . . 4
6 sseq1 3525 . . . . 5
76biimpar 485 . . . 4
84, 5, 7syl2an 477 . . 3
98exlimiv 1698 . 2
103, 9sylbi 195 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   w3a 973   wceq 1379  wex 1596   wcel 1767  cab 2452  wral 2814   wss 3476   cdm 4999   cres 5001   wfn 5581  cfv 5586  (class class class)co 6282  cpred 28820 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-br 4448  df-opab 4506  df-xp 5005  df-rel 5006  df-cnv 5007  df-co 5008  df-dm 5009  df-rn 5010  df-res 5011  df-ima 5012  df-iota 5549  df-fun 5588  df-fn 5589  df-fv 5594  df-ov 6285  df-pred 28821 This theorem is referenced by:  frrlem5  28968  frrlem5d  28971  frrlem7  28974
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