Theorem spsd 1956

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 1948	. 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 1453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-12 1944

This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1675

This theorem is referenced by:  axc11nlem  2032  axc11nlemALT  2153  equveli  2191  nfsb4t  2229  mo2v  2317  moexex  2381  2eu6  2398  zorn2lem4  8960  zorn2lem5  8961  axpowndlem3  9055  axacndlem5  9067  bj-axc11nlemv  31393  wl-equsal1i  31922  axc5c4c711  36797