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Theorem nfcnv 4968
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 4797 . 2  |-  `' A  =  { <. y ,  z
>.  |  z A
y }
2 nfcv 2563 . . . 4  |-  F/_ x
z
3 nfcnv.1 . . . 4  |-  F/_ x A
4 nfcv 2563 . . . 4  |-  F/_ x
y
52, 3, 4nfbr 4404 . . 3  |-  F/ x  z A y
65nfopab 4425 . 2  |-  F/_ x { <. y ,  z
>.  |  z A
y }
71, 6nfcxfr 2561 1  |-  F/_ x `' A
Colors of variables: wff setvar class
Syntax hints:   F/_wnfc 2550   class class class wbr 4359   {copab 4417   `'ccnv 4788
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2058  ax-ext 2402
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2552  df-rab 2717  df-v 3018  df-dif 3375  df-un 3377  df-in 3379  df-ss 3386  df-nul 3698  df-if 3848  df-sn 3935  df-pr 3937  df-op 3941  df-br 4360  df-opab 4419  df-cnv 4797
This theorem is referenced by:  nfrn  5032  nfpred  5340  nffun  5559  nff1  5730  nfsup  7911  nfinf  7944  gsumcom2  17543  ptbasfi  20531  mbfposr  22543  itg1climres  22607  funcnvmptOLD  28209  funcnvmpt  28210  nfwsuc  30445  nfwlim  30449  aomclem8  35826  rfcnpre1  37250  rfcnpre2  37262
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