Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-nfalt Structured version   Unicode version

Theorem bj-nfalt 30829
Description: Closed form of nfal 1975. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-nfalt  |-  ( A. x F/ y ph  ->  F/ y A. x ph )

Proof of Theorem bj-nfalt
StepHypRef Expression
1 bj-hbalt 30804 . . . 4  |-  ( A. x ( ph  ->  A. y ph )  -> 
( A. x ph  ->  A. y A. x ph ) )
21alimi 1654 . . 3  |-  ( A. y A. x ( ph  ->  A. y ph )  ->  A. y ( A. x ph  ->  A. y A. x ph ) )
32alcoms 1867 . 2  |-  ( A. x A. y ( ph  ->  A. y ph )  ->  A. y ( A. x ph  ->  A. y A. x ph ) )
4 df-nf 1638 . . 3  |-  ( F/ y ph  <->  A. y
( ph  ->  A. y ph ) )
54albii 1661 . 2  |-  ( A. x F/ y ph  <->  A. x A. y ( ph  ->  A. y ph ) )
6 df-nf 1638 . 2  |-  ( F/ y A. x ph  <->  A. y ( A. x ph  ->  A. y A. x ph ) )
73, 5, 63imtr4i 266 1  |-  ( A. x F/ y ph  ->  F/ y A. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1403   F/wnf 1637
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-11 1866
This theorem depends on definitions:  df-bi 185  df-nf 1638
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator