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Theorem nfeqd 2192
 Description: Hypothesis builder for equality. (Contributed by Mario Carneiro, 7-Oct-2016.)
Hypotheses
Ref Expression
nfeqd.1
nfeqd.2
Assertion
Ref Expression
nfeqd

Proof of Theorem nfeqd
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfcleq 2034 . 2
2 nfv 1421 . . 3
3 nfeqd.1 . . . . 5
43nfcrd 2191 . . . 4
5 nfeqd.2 . . . . 5
65nfcrd 2191 . . . 4
74, 6nfbid 1480 . . 3
82, 7nfald 1643 . 2
91, 8nfxfrd 1364 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241   wceq 1243  wnf 1349   wcel 1393  wnfc 2165 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 1336  ax-7 1337  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-cleq 2033  df-nfc 2167 This theorem is referenced by:  nfeld  2193  nfned  2298  vtoclgft  2604  sbcralt  2834  sbcrext  2835  csbiebt  2886  dfnfc2  3598  eusvnfb  4186  eusv2i  4187  iota2df  4891  riota5f  5492
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