Theorem r19.37av 2623

Description: Restricted version of one direction of Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 2-Apr-2004.)

Assertion

Ref	Expression
r19.37av	|- ( E. x e. A ( ph -> ps ) -> ( ph -> E. x e. A ps ) )

Distinct variable group:   ph, x

Allowed substitution hints:   ps( x)   A( x)

Proof of Theorem r19.37av

Step	Hyp	Ref	Expression
1		nfv 1521	. 2 |- F/ x ph
2	1	r19.37 2622	1 |- ( E. x e. A ( ph -> ps ) -> ( ph -> E. x e. A ps ) )

Syntax hints:   -> wi 4   E.wrex 2449

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-17 1519  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-ral 2453  df-rex 2454

This theorem is referenced by:  ssiun  3915