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Theorem nfcnv 5010
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 4845 . 2  |-  `' A  =  { <. y ,  z
>.  |  z A
y }
2 nfcv 2540 . . . 4  |-  F/_ x
z
3 nfcnv.1 . . . 4  |-  F/_ x A
4 nfcv 2540 . . . 4  |-  F/_ x
y
52, 3, 4nfbr 4216 . . 3  |-  F/ x  z A y
65nfopab 4233 . 2  |-  F/_ x { <. y ,  z
>.  |  z A
y }
71, 6nfcxfr 2537 1  |-  F/_ x `' A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2527   class class class wbr 4172   {copab 4225   `'ccnv 4836
This theorem is referenced by:  nfrn  5071  nffun  5435  nff1  5596  nfsup  7412  gsumcom2  15504  ptbasfi  17566  mbfposr  19497  itg1climres  19559  funcnvmptOLD  24035  funcnvmpt  24036  aomclem8  27027  rfcnpre1  27557  rfcnpre2  27569
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-br 4173  df-opab 4227  df-cnv 4845
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