Theorem 19.36i 1665

Description: Inference from Theorem 19.36 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 2-Feb-2015.)

Hypotheses

Ref	Expression
19.36i.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	. . 3 |- E. x ( ph -> ps )
2	1	19.35i 1618	. 2 |- ( A. x ph -> E. x ps )
3		19.36i.1	. . 3 |- F/ x ps
4		id 19	. . 3 |- ( ps -> ps )
5	3, 4	exlimi 1587	. 2 |- ( E. x ps -> ps )
6	2, 5	syl 14	1 |- ( A. x ph -> ps )

Syntax hints:   -> wi 4   A.wal 1346   F/wnf 1453   E.wex 1485

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-nf 1454

This theorem is referenced by:  spimfv  1692  19.36aiv  1894  vtoclf  2783