Theorem 19.36i 2099

Description: Inference associated with 19.36 2098. See 19.36iv 1905 for a version requiring fewer axioms. (Contributed by NM, 24-Jun-1993.)

Hypotheses

Ref	Expression
19.36.1	|- F/ x ps
19.36i.2	|- E. x ( ph -> ps )

Assertion

Ref	Expression
19.36i	|- ( A. x ph -> ps )

Proof of Theorem 19.36i

Step	Hyp	Ref	Expression
1		19.36i.2	. 2 |- E. x ( ph -> ps )
2		19.36.1	. . 3 |- F/ x ps
3	2	19.36 2098	. 2 |- ( E. x ( ph -> ps ) <-> ( A. x ph -> ps ) )
4	1, 3	mpbi 220	1 |- ( A. x ph -> ps )

Syntax hints:   -> wi 4   A.wal 1481   E.wex 1704   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nf 1710

This theorem is referenced by:  spimv1  2115  spim  2254  vtoclf  3258  bj-vtoclf  32908