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Theorem nfcnv 4860
Description: Bound-variable hypothesis builder for converse. (Contributed by NM, 31-Jan-2004.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
nfcnv.1  |-  F/_ x A
Assertion
Ref Expression
nfcnv  |-  F/_ x `' A

Proof of Theorem nfcnv
Dummy variables  y 
z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-cnv 4697 . 2  |-  `' A  =  { <. y ,  z
>.  |  z A
y }
2 nfcv 2419 . . . 4  |-  F/_ x
z
3 nfcnv.1 . . . 4  |-  F/_ x A
4 nfcv 2419 . . . 4  |-  F/_ x
y
52, 3, 4nfbr 4067 . . 3  |-  F/ x  z A y
65nfopab 4084 . 2  |-  F/_ x { <. y ,  z
>.  |  z A
y }
71, 6nfcxfr 2416 1  |-  F/_ x `' A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2406   class class class wbr 4023   {copab 4076   `'ccnv 4688
This theorem is referenced by:  nfrn  4921  nffun  5277  nff1  5435  nfsup  7202  gsumcom2  15226  ptbasfi  17276  mbfposr  19007  itg1climres  19069  funcnvmptOLD  23234  funcnvmpt  23235  trinv  25395  ltrinvlem  25406  aomclem8  27159  rfcnpre1  27690  rfcnpre2  27702
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-cnv 4697
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