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Theorem bnd 6233
Description: A very strong generalization of the Axiom of Replacement (compare zfrep6 4800), derived from the Collection Principle cp 6232. 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 6232 . . 3
2 ralim 2200 . . . 4
32eximi 1373 . . 3
41, 3ax-mp 8 . 2
5419.37aiv 1739 1
Colors of variables: wff set class
Syntax hints:   wi 4  wex 1346  wral 2138  wrex 2139
This theorem is referenced by:  bnd2 6234
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1342  ax-6 1343  ax-7 1344  ax-gen 1345  ax-8 1429  ax-10 1430  ax-11 1431  ax-12 1432  ax-13 1433  ax-14 1434  ax-17 1441  ax-9 1456  ax-4 1462  ax-16 1640  ax-ext 1911  ax-rep 3444  ax-sep 3454  ax-nul 3463  ax-pow 3499  ax-pr 3523  ax-un 3795  ax-reg 6043  ax-inf2 6078
This theorem depends on definitions:  df-bi 175  df-or 361  df-an 362  df-3or 913  df-3an 914  df-ex 1347  df-sb 1602  df-eu 1829  df-mo 1830  df-clab 1917  df-cleq 1922  df-clel 1925  df-ne 2049  df-ral 2142  df-rex 2143  df-rab 2145  df-v 2337  df-sbc 2502  df-csb 2577  df-dif 2637  df-un 2639  df-in 2641  df-ss 2643  df-pss 2645  df-nul 2900  df-if 3005  df-pw 3063  df-sn 3080  df-pr 3081  df-tp 3082  df-op 3083  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 3649  df-we 3665  df-ord 3681  df-on 3682  df-lim 3683  df-suc 3684  df-om 3958  df-xp 4005  df-rel 4006  df-cnv 4007  df-co 4008  df-dm 4009  df-rn 4010  df-res 4011  df-ima 4012  df-fun 4013  df-fn 4014  df-f 4015  df-fv 4019  df-mpt 5063  df-rdg 5363  df-r1 6119  df-rank 6120
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