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Theorem nfceqdf 2174
Description: An equality theorem for effectively not free. (Contributed by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
nfceqdf.1  F/
nfceqdf.2
Assertion
Ref Expression
nfceqdf  F/_ 
F/_

Proof of Theorem nfceqdf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfceqdf.1 . . . 4  F/
2 nfceqdf.2 . . . . 5
32eleq2d 2104 . . . 4
41, 3nfbidf 1429 . . 3  F/  F/
54albidv 1702 . 2  F/  F/
6 df-nfc 2164 . 2  F/_  F/
7 df-nfc 2164 . 2  F/_  F/
85, 6, 73bitr4g 212 1  F/_ 
F/_
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240   wceq 1242   F/wnf 1346   wcel 1390   F/_wnfc 2162
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-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-cleq 2030  df-clel 2033  df-nfc 2164
This theorem is referenced by:  nfopd  3557  dfnfc2  3589  nfimad  4620  nffvd  5130
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