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Theorem nfcnv 5053
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 4888 . 2  |-  `' A  =  { <. y ,  z
>.  |  z A
y }
2 nfcv 2574 . . . 4  |-  F/_ x
z
3 nfcnv.1 . . . 4  |-  F/_ x A
4 nfcv 2574 . . . 4  |-  F/_ x
y
52, 3, 4nfbr 4258 . . 3  |-  F/ x  z A y
65nfopab 4275 . 2  |-  F/_ x { <. y ,  z
>.  |  z A
y }
71, 6nfcxfr 2571 1  |-  F/_ x `' A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2561   class class class wbr 4214   {copab 4267   `'ccnv 4879
This theorem is referenced by:  nfrn  5114  nffun  5478  nff1  5639  nfsup  7458  gsumcom2  15551  ptbasfi  17615  mbfposr  19546  itg1climres  19608  funcnvmptOLD  24084  funcnvmpt  24085  nfpred  25446  nfwsuc  25571  nfwlim  25575  aomclem8  27138  rfcnpre1  27668  rfcnpre2  27680
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215  df-opab 4269  df-cnv 4888
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