ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  alimdv Unicode version

Theorem alimdv 1872
Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 3-Apr-1994.)
Hypothesis
Ref Expression
alimdv.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
alimdv  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)

Proof of Theorem alimdv
StepHypRef Expression
1 ax-17 1519 . 2  |-  ( ph  ->  A. x ph )
2 alimdv.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2alimdh 1460 1  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1346
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1440  ax-gen 1442  ax-17 1519
This theorem is referenced by:  2alimdv  1874  moim  2083  ralimdv2  2540  sstr2  3154  reuss2  3407  ssuni  3818  disjss2  3969  disjss1  3972  disjiun  3984  exmidsssnc  4189  soss  4299  alxfr  4446  ssrel  4699  ssrel2  4701  ssrelrel  4711  iotaval  5171  omnimkv  7132
  Copyright terms: Public domain W3C validator