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Theorem nfcnv 4603
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 4436 . 2  |-  `' A  =  { <. y ,  z
>.  |  z A
y }
2 nfcv 2228 . . . 4  |-  F/_ x
z
3 nfcnv.1 . . . 4  |-  F/_ x A
4 nfcv 2228 . . . 4  |-  F/_ x
y
52, 3, 4nfbr 3881 . . 3  |-  F/ x  z A y
65nfopab 3898 . 2  |-  F/_ x { <. y ,  z
>.  |  z A
y }
71, 6nfcxfr 2225 1  |-  F/_ x `' A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2215   class class class wbr 3837   {copab 3890   `'ccnv 4427
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3001  df-sn 3447  df-pr 3448  df-op 3450  df-br 3838  df-opab 3892  df-cnv 4436
This theorem is referenced by:  nfrn  4668  nffun  5024  nff1  5198  nfinf  6691
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