Theorem spsd 1917

Description: Deduction generalizing antecedent. (Contributed by NM, 17-Aug-1994.)

Hypothesis

Ref	Expression
spsd.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
spsd	|- ( ph -> ( A. x ps -> ch ) )

Proof of Theorem spsd

Step	Hyp	Ref	Expression
1		sp 1909	. 2 |- ( A. x ps -> ps )
2		spsd.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	syl5 33	1 |- ( ph -> ( A. x ps -> ch ) )

Syntax hints:   -> wi 4   A.wal 1435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-12 1904

This theorem depends on definitions:  df-bi 188  df-ex 1660

This theorem is referenced by:  axc11nlem  1993  axc11nlemOLD  2101  equveli  2141  nfsb4t  2181  mo2v  2270  mo2vOLD  2271  moexex  2335  2eu6  2354  zorn2lem4  8918  zorn2lem5  8919  axpowndlem3  9013  axacndlem5  9025  bj-axc11nlemv  31136  wl-equsal1i  31624  axc5c4c711  36437