Theorem 19.35i 1604

Description: Inference from Theorem 19.35 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 2-Feb-2015.)

Hypothesis

Ref	Expression
19.35i.1	|- E. x ( ph -> ps )

Assertion

Ref	Expression
19.35i	|- ( A. x ph -> E. x ps )

Proof of Theorem 19.35i

Step	Hyp	Ref	Expression
1		19.35i.1	. 2 |- E. x ( ph -> ps )
2		19.35-1 1603	. 2 |- ( E. x ( ph -> ps ) -> ( A. x ph -> E. x ps ) )
3	1, 2	ax-mp 5	1 |- ( A. x ph -> E. x ps )

Syntax hints:   -> wi 4   A.wal 1329   E.wex 1468

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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  19.36i  1650  spimed  1718