Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  hbalg Structured version   Unicode version

Theorem hbalg 28642
Description: Closed form of hbal 1751. Derived from hbalgVD 29017. (Contributed by Alan Sare, 8-Feb-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
hbalg  |-  ( A. y ( ph  ->  A. x ph )  ->  A. y ( A. y ph  ->  A. x A. y ph ) )

Proof of Theorem hbalg
StepHypRef Expression
1 alim 1567 . . 3  |-  ( A. y ( ph  ->  A. x ph )  -> 
( A. y ph  ->  A. y A. x ph ) )
2 ax-7 1749 . . 3  |-  ( A. y A. x ph  ->  A. x A. y ph )
31, 2syl6 31 . 2  |-  ( A. y ( ph  ->  A. x ph )  -> 
( A. y ph  ->  A. x A. y ph ) )
43a5i 1807 1  |-  ( A. y ( ph  ->  A. x ph )  ->  A. y ( A. y ph  ->  A. x A. y ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549
This theorem is referenced by:  hbexgVD  29018
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-ex 1551  df-nf 1554
  Copyright terms: Public domain W3C validator