Theorem bnj1238 30877

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypothesis

Ref	Expression
bnj1238.1	|- ( ph <-> E. x e. A ( ps /\ ch ) )

Assertion

Ref	Expression
bnj1238	|- ( ph -> E. x e. A ps )

Proof of Theorem bnj1238

Step	Hyp	Ref	Expression
1		bnj1238.1	. 2 |- ( ph <-> E. x e. A ( ps /\ ch ) )
2		bnj1239 30876	. 2 |- ( E. x e. A ( ps /\ ch ) -> E. x e. A ps )
3	1, 2	sylbi 207	1 |- ( ph -> E. x e. A ps )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384   E.wrex 2913

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-ral 2917  df-rex 2918

This theorem is referenced by:  bnj1245  31082  bnj1256  31083  bnj1259  31084  bnj1311  31092  bnj1371  31097