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Theorem nfeqd 2170
Description: Hypothesis builder for equality. (Contributed by Mario Carneiro, 7-Oct-2016.)
Hypotheses
Ref Expression
nfeqd.1  F/_
nfeqd.2  F/_
Assertion
Ref Expression
nfeqd  F/

Proof of Theorem nfeqd
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfcleq 2012 . 2
2 nfv 1398 . . 3  F/
3 nfeqd.1 . . . . 5  F/_
43nfcrd 2169 . . . 4  F/
5 nfeqd.2 . . . . 5  F/_
65nfcrd 2169 . . . 4  F/
74, 6nfbid 1458 . . 3  F/
82, 7nfald 1621 . 2  F/
91, 8nfxfrd 1340 1  F/
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1224   wceq 1226   F/wnf 1325   wcel 1370   F/_wnfc 2143
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 1312  ax-7 1313  ax-gen 1314  ax-4 1377  ax-17 1396  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-nf 1326  df-cleq 2011  df-nfc 2145
This theorem is referenced by:  nfeld  2171  nfned  2272  vtoclgft  2577  sbcralt  2807  sbcrext  2808  csbiebt  2859  dfnfc2  3568  eusvnfb  4132  eusv2i  4133  iota2df  4814  riota5f  5412
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