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  2026  hbsb4t  2067  mopick  2159  eupickbi  2163  ceqsalg  2842  mo2icl  2996  reu6  3006  sbcal  3094  csbie2t  3187  dfss4st  3454  reldisj  3560  dfnfc2  3932  ssopab2  4394  eusvnfb  4575  mosubopt  4815  issref  5145  fv3  5693  fvmptt  5769  fnoprabg  6154  bj-exlimmp  16541  strcollnft  16754