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Theorem nfcnv 4876
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 4713 . 2  |-  `' A  =  { <. y ,  z
>.  |  z A
y }
2 nfcv 2432 . . . 4  |-  F/_ x
z
3 nfcnv.1 . . . 4  |-  F/_ x A
4 nfcv 2432 . . . 4  |-  F/_ x
y
52, 3, 4nfbr 4083 . . 3  |-  F/ x  z A y
65nfopab 4100 . 2  |-  F/_ x { <. y ,  z
>.  |  z A
y }
71, 6nfcxfr 2429 1  |-  F/_ x `' A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2419   class class class wbr 4039   {copab 4092   `'ccnv 4704
This theorem is referenced by:  nfrn  4937  nffun  5293  nff1  5451  nfsup  7218  gsumcom2  15242  ptbasfi  17292  mbfposr  19023  itg1climres  19085  funcnvmptOLD  23249  funcnvmpt  23250  trinv  25498  ltrinvlem  25509  aomclem8  27262  rfcnpre1  27793  rfcnpre2  27805
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-cnv 4713
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