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Theorem bnj1522 29147
 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 2404 . 2
9 biid 228 . 2
101, 2, 3, 4, 5, 6, 7, 8, 9bnj1523 29146 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   w3a 936   wceq 1649   wcel 1721  cab 2390   wne 2567  wral 2666  wrex 2667  crab 2670   wss 3280  cop 3777  cuni 3975   class class class wbr 4172   cres 4839   wfn 5408  cfv 5413   c-bnj14 28758   w-bnj15 28762 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-13 1723  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-rep 4280  ax-sep 4290  ax-nul 4298  ax-pow 4337  ax-pr 4363  ax-un 4660  ax-reg 7516  ax-inf2 7552 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258  df-mo 2259  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-ral 2671  df-rex 2672  df-reu 2673  df-rab 2675  df-v 2918  df-sbc 3122  df-csb 3212  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-pss 3296  df-nul 3589  df-if 3700  df-pw 3761  df-sn 3780  df-pr 3781  df-tp 3782  df-op 3783  df-uni 3976  df-iun 4055  df-br 4173  df-opab 4227  df-mpt 4228  df-tr 4263  df-eprel 4454  df-id 4458  df-po 4463  df-so 4464  df-fr 4501  df-we 4503  df-ord 4544  df-on 4545  df-lim 4546  df-suc 4547  df-om 4805  df-xp 4843  df-rel 4844  df-cnv 4845  df-co 4846  df-dm 4847  df-rn 4848  df-res 4849  df-ima 4850  df-iota 5377  df-fun 5415  df-fn 5416  df-f 5417  df-f1 5418  df-fo 5419  df-f1o 5420  df-fv 5421  df-1o 6683  df-bnj17 28757  df-bnj14 28759  df-bnj13 28761  df-bnj15 28763  df-bnj18 28765  df-bnj19 28767
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