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Theorem frrlem3 25589
 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 25587 . . 3
32abeq2i 2545 . 2
4 fndm 5547 . . . 4
5 simp1 958 . . . 4
6 sseq1 3371 . . . . 5
76biimpar 473 . . . 4
84, 5, 7syl2an 465 . . 3
98exlimiv 1645 . 2
103, 9sylbi 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937  wex 1551   wceq 1653   wcel 1726  cab 2424  wral 2707   wss 3322   cdm 4881   cres 4883   wfn 5452  cfv 5457  (class class class)co 6084  cpred 25443 This theorem is referenced by:  frrlem5  25591  frrlem5d  25594  frrlem7  25597 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-opab 4270  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894  df-iota 5421  df-fun 5459  df-fn 5460  df-fv 5465  df-ov 6087  df-pred 25444
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