Theorem ax5d 1840

Description: ax-5 1839 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

Step	Hyp	Ref	Expression
1		ax-5 1839	. 2 |- ( ps -> A. x ps )
2	1	a1i 11	1 |- ( ph -> ( ps -> A. x ps ) )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-5 1839

This theorem is referenced by:  aevlemOLD  1989  ax13w  2013