Theorem 19.37aiv 1565

Description: Inference from Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
19.37aiv.1	|- E. x ( ph -> ps )

Assertion

Ref	Expression
19.37aiv	|- ( ph -> E. x ps )

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem 19.37aiv

Step	Hyp	Ref	Expression
1		19.37aiv.1	. 2 |- E. x ( ph -> ps )
2		nfv 1421	. . 3 |- F/ x ph
3	2	19.37-1 1564	. 2 |- ( E. x ( ph -> ps ) -> ( ph -> E. x ps ) )
4	1, 3	ax-mp 7	1 |- ( ph -> E. x ps )

Syntax hints:   -> wi 4   E.wex 1381

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350

This theorem is referenced by:  eqvinc  2667  limom  4336