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Theorem nfcnv 4808
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 4636 . 2  |-  `' A  =  { <. y ,  z
>.  |  z A
y }
2 nfcv 2319 . . . 4  |-  F/_ x
z
3 nfcnv.1 . . . 4  |-  F/_ x A
4 nfcv 2319 . . . 4  |-  F/_ x
y
52, 3, 4nfbr 4051 . . 3  |-  F/ x  z A y
65nfopab 4073 . 2  |-  F/_ x { <. y ,  z
>.  |  z A
y }
71, 6nfcxfr 2316 1  |-  F/_ x `' A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2306   class class class wbr 4005   {copab 4065   `'ccnv 4627
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2741  df-un 3135  df-sn 3600  df-pr 3601  df-op 3603  df-br 4006  df-opab 4067  df-cnv 4636
This theorem is referenced by:  nfrn  4874  nffun  5241  nff1  5421  nfinf  7018
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