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Theorem nfcnv 5033
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 4862 . 2  |-  `' A  =  { <. y ,  z
>.  |  z A
y }
2 nfcv 2591 . . . 4  |-  F/_ x
z
3 nfcnv.1 . . . 4  |-  F/_ x A
4 nfcv 2591 . . . 4  |-  F/_ x
y
52, 3, 4nfbr 4470 . . 3  |-  F/ x  z A y
65nfopab 4491 . 2  |-  F/_ x { <. y ,  z
>.  |  z A
y }
71, 6nfcxfr 2589 1  |-  F/_ x `' A
Colors of variables: wff setvar class
Syntax hints:   F/_wnfc 2577   class class class wbr 4426   {copab 4483   `'ccnv 4853
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-br 4427  df-opab 4485  df-cnv 4862
This theorem is referenced by:  nfrn  5097  nfpred  5404  nffun  5623  nff1  5794  nfsup  7971  nfinf  8004  gsumcom2  17542  ptbasfi  20527  mbfposr  22485  itg1climres  22549  funcnvmptOLD  28110  funcnvmpt  28111  nfwsuc  30288  nfwlim  30292  aomclem8  35625  rfcnpre1  36980  rfcnpre2  36992
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