MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax5d Structured version   Unicode version

Theorem ax5d 1752
Description: ax-5 1751 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders. (Contributed by NM, 1-Mar-2013.)
Assertion
Ref Expression
ax5d  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Distinct variable group:    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem ax5d
StepHypRef Expression
1 ax-5 1751 . 2  |-  ( ps 
->  A. x ps )
21a1i 11 1  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-5 1751
This theorem is referenced by:  ax13w  1884  aevlem1  1997  bj-axc11nlemv  31095  bj-axc15v  31110
  Copyright terms: Public domain W3C validator