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Theorem bnd 6309
Description: A very strong generalization of the Axiom of Replacement (compare zfrep6 4819), derived from the Collection Principle cp 6308. Its strength lies in the rather profound fact that does not have to be a "function-like" wff, as it does in the standard Axiom of Replacement. This theorem is sometimes called the Boundedness Axiom.
Assertion
Ref Expression
bnd
Distinct variable groups:   ,,   ,,,
Allowed substitution hints:   (,)

Proof of Theorem bnd
StepHypRef Expression
1 cp 6308 . . 3
2 ralim 2187 . . . 4
32eximi 1361 . . 3
41, 3ax-mp 8 . 2
5419.37aiv 1727 1
Colors of variables: wff set class
Syntax hints:   wi 4  wex 1334  wral 2125  wrex 2126
This theorem is referenced by:  bnd2 6310
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1330  ax-6 1331  ax-7 1332  ax-gen 1333  ax-8 1417  ax-10 1418  ax-11 1419  ax-12 1420  ax-13 1421  ax-14 1422  ax-17 1429  ax-9 1444  ax-4 1450  ax-16 1628  ax-ext 1899  ax-rep 3444  ax-sep 3454  ax-nul 3463  ax-pow 3499  ax-pr 3523  ax-un 3797  ax-reg 6119  ax-inf2 6154
This theorem depends on definitions:  df-bi 174  df-or 357  df-an 358  df-3or 899  df-3an 900  df-ex 1335  df-sb 1590  df-eu 1817  df-mo 1818  df-clab 1905  df-cleq 1910  df-clel 1913  df-ne 2036  df-ral 2129  df-rex 2130  df-rab 2132  df-v 2324  df-sbc 2491  df-csb 2573  df-dif 2635  df-un 2637  df-in 2639  df-ss 2641  df-pss 2643  df-nul 2899  df-if 3004  df-pw 3062  df-sn 3079  df-pr 3080  df-tp 3081  df-op 3082  df-uni 3214  df-int 3248  df-iun 3286  df-iin 3287  df-br 3359  df-opab 3413  df-tr 3428  df-eprel 3608  df-id 3611  df-po 3616  df-so 3630  df-fr 3650  df-we 3666  df-ord 3682  df-on 3683  df-lim 3684  df-suc 3685  df-om 3962  df-xp 4009  df-rel 4010  df-cnv 4011  df-co 4012  df-dm 4013  df-rn 4014  df-res 4015  df-ima 4016  df-fun 4017  df-fn 4018  df-f 4019  df-fv 4023  df-mpt 5106  df-rdg 5424  df-r1 6195  df-rank 6196
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