Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfceqdf Structured version   Unicode version

Theorem nfceqdf 2573
 Description: An equality theorem for effectively not free. (Contributed by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
nfceqdf.1
nfceqdf.2
Assertion
Ref Expression
nfceqdf

Proof of Theorem nfceqdf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfceqdf.1 . . . 4
2 nfceqdf.2 . . . . 5
32eleq2d 2505 . . . 4
41, 3nfbidf 1791 . . 3
54albidv 1636 . 2
6 df-nfc 2563 . 2
7 df-nfc 2563 . 2
85, 6, 73bitr4g 281 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550  wnf 1554   wceq 1653   wcel 1726  wnfc 2561 This theorem is referenced by:  nfopd  4003  dfnfc2  4035  nfimad  5215  nffvd  5740  riotasvdOLD  6596  riotasv2d  6597  riotasv2dOLD  6598  riotasv3dOLD  6602 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555  df-cleq 2431  df-clel 2434  df-nfc 2563
 Copyright terms: Public domain W3C validator