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Theorem nfbidf 1429
Description: An equality theorem for effectively not free. (Contributed by Mario Carneiro, 4-Oct-2016.)
Hypotheses
Ref Expression
nfbidf.1  F/
nfbidf.2
Assertion
Ref Expression
nfbidf  F/  F/

Proof of Theorem nfbidf
StepHypRef Expression
1 nfbidf.1 . . . 4  F/
21nfri 1409 . . 3
3 nfbidf.2 . . . 4
42, 3albidh 1366 . . . 4
53, 4imbi12d 223 . . 3
62, 5albidh 1366 . 2
7 df-nf 1347 . 2  F/
8 df-nf 1347 . 2  F/
96, 7, 83bitr4g 212 1  F/  F/
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240   F/wnf 1346
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  dvelimdf  1889  nfcjust  2163  nfceqdf  2174
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