Theorem sps 1583

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 1557	. 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 1393

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1556

This theorem is referenced by:  19.21ht  1627  exim  1645  alexdc  1665  19.2  1684  ax10o  1761  hbae  1764  cbv1h  1792  equvini  1804  equveli  1805  ax10oe  1843  drex1  1844  drsb1  1845  exdistrfor  1846  ax11v2  1866  equs5or  1876  sbequi  1885  drsb2  1887  spsbim  1889  sbcomxyyz  2023  hbsb4t  2064  mopick  2156  eupickbi  2160  ceqsalg  2829  mo2icl  2983  reu6  2993  sbcal  3081  csbie2t  3174  dfss4st  3438  reldisj  3544  dfnfc2  3909  ssopab2  4368  eusvnfb  4549  mosubopt  4789  issref  5117  fv3  5658  fvmptt  5734  fnoprabg  6117  bj-exlimmp  16301  strcollnft  16515