MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  a17d Structured version   Unicode version

Theorem a17d 1628
Description: ax-17 1627 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders. (Contributed by NM, 1-Mar-2013.)
Assertion
Ref Expression
a17d  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Distinct variable group:    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem a17d
StepHypRef Expression
1 ax-17 1627 . 2  |-  ( ps 
->  A. x ps )
21a1i 11 1  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1550
This theorem is referenced by:  ax12w  1740  dvelimvOLD  2029  dvelimvNEW7  29463
This theorem was proved from axioms:  ax-1 5  ax-mp 8  ax-17 1627
  Copyright terms: Public domain W3C validator