Theorem sps 1586

Description: Generalization of antecedent. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
sps.1	|- ( ph -> ps )

Assertion

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

Proof of Theorem sps

Step	Hyp	Ref	Expression
1		sp 1560	. 2 |- ( A. x ph -> ph )
2		sps.1	. 2 |- ( ph -> ps )
3	1, 2	syl 14	1 |- ( A. x ph -> ps )

Syntax hints:   -> wi 4   A.wal 1396

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1559

This theorem is referenced by:  19.21ht  1630  exim  1648  alexdc  1668  19.2  1687  ax10o  1763  hbae  1766  cbv1h  1795  equvini  1807  equveli  1808  ax10oe  1846  drex1  1847  drsb1  1848  exdistrfor  1849  ax11v2  1869  equs5or  1879  sbequi  1888  drsb2  1890  spsbim  1892  sbcomxyyz  2028  hbsb4t  2069  mopick  2161  eupickbi  2165  ceqsalg  2844  mo2icl  2998  reu6  3008  sbcal  3096  csbie2t  3189  dfss4st  3456  reldisj  3562  dfnfc2  3934  ssopab2  4396  eusvnfb  4577  mosubopt  4817  issref  5147  fv3  5695  fvmptt  5771  fnoprabg  6156  bj-exlimmp  16558  strcollnft  16771