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Theorem nfcnv 4686
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 4515 . 2  |-  `' A  =  { <. y ,  z
>.  |  z A
y }
2 nfcv 2256 . . . 4  |-  F/_ x
z
3 nfcnv.1 . . . 4  |-  F/_ x A
4 nfcv 2256 . . . 4  |-  F/_ x
y
52, 3, 4nfbr 3942 . . 3  |-  F/ x  z A y
65nfopab 3964 . 2  |-  F/_ x { <. y ,  z
>.  |  z A
y }
71, 6nfcxfr 2253 1  |-  F/_ x `' A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2243   class class class wbr 3897   {copab 3956   `'ccnv 4506
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502  df-op 3504  df-br 3898  df-opab 3958  df-cnv 4515
This theorem is referenced by:  nfrn  4752  nffun  5114  nff1  5294  nfinf  6870
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