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Theorem bnj1522 29441
 Description: Well-founded recursion, part 3 of 3. The proof has been taken from Chapter 4 of Don Monk's notes on Set Theory. See http://euclid.colorado.edu/~monkd/setth.pdf. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1522.1
bnj1522.2
bnj1522.3
bnj1522.4
Assertion
Ref Expression
bnj1522
Distinct variable groups:   ,,,   ,   ,,,   ,   ,,,   ,
Allowed substitution hints:   (,)   (,,)   (,,)   (,)   (,)

Proof of Theorem bnj1522
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bnj1522.1 . 2
2 bnj1522.2 . 2
3 bnj1522.3 . 2
4 bnj1522.4 . 2
5 biid 228 . 2
6 biid 228 . 2
7 biid 228 . 2
8 eqid 2436 . 2
9 biid 228 . 2
101, 2, 3, 4, 5, 6, 7, 8, 9bnj1523 29440 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   w3a 936   wceq 1652   wcel 1725  cab 2422   wne 2599  wral 2705  wrex 2706  crab 2709   wss 3320  cop 3817  cuni 4015   class class class wbr 4212   cres 4880   wfn 5449  cfv 5454   c-bnj14 29052   w-bnj15 29056 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-rep 4320  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701  ax-reg 7560  ax-inf2 7596 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-reu 2712  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-pss 3336  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-tp 3822  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-mpt 4268  df-tr 4303  df-eprel 4494  df-id 4498  df-po 4503  df-so 4504  df-fr 4541  df-we 4543  df-ord 4584  df-on 4585  df-lim 4586  df-suc 4587  df-om 4846  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-fo 5460  df-f1o 5461  df-fv 5462  df-1o 6724  df-bnj17 29051  df-bnj14 29053  df-bnj13 29055  df-bnj15 29057  df-bnj18 29059  df-bnj19 29061
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