Theorem r19.37av 2508

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 1462	. 2 |- F/ x ph
2	1	r19.37 2507	1 |- ( E. x e. A ( ph -> ps ) -> ( ph -> E. x e. A ps ) )

Syntax hints:   -> wi 4   E.wrex 2350

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-ral 2354  df-rex 2355

This theorem is referenced by:  ssiun  3728