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Theorem nfcnv 4758
 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
Assertion
Ref Expression
nfcnv

Proof of Theorem nfcnv
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-cnv 4587 . 2
2 nfcv 2296 . . . 4
3 nfcnv.1 . . . 4
4 nfcv 2296 . . . 4
52, 3, 4nfbr 4006 . . 3
65nfopab 4028 . 2
71, 6nfcxfr 2293 1
 Colors of variables: wff set class Syntax hints:  wnfc 2283   class class class wbr 3961  copab 4020  ccnv 4578 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711  df-un 3102  df-sn 3562  df-pr 3563  df-op 3565  df-br 3962  df-opab 4022  df-cnv 4587 This theorem is referenced by:  nfrn  4824  nffun  5186  nff1  5366  nfinf  6949
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