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Theorem nfcnv 4542
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 4381 . 2  |-  `' A  =  { <. y ,  z
>.  |  z A
y }
2 nfcv 2194 . . . 4  |-  F/_ x
z
3 nfcnv.1 . . . 4  |-  F/_ x A
4 nfcv 2194 . . . 4  |-  F/_ x
y
52, 3, 4nfbr 3836 . . 3  |-  F/ x  z A y
65nfopab 3853 . 2  |-  F/_ x { <. y ,  z
>.  |  z A
y }
71, 6nfcxfr 2191 1  |-  F/_ x `' A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2181   class class class wbr 3792   {copab 3845   `'ccnv 4372
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-op 3412  df-br 3793  df-opab 3847  df-cnv 4381
This theorem is referenced by:  nfrn  4607  nffun  4952  nff1  5118
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