Theorem bnj1265 30883

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

Hypothesis

Ref	Expression
bnj1265.1	|- ( ph -> E. x e. A ps )

Assertion

Ref	Expression
bnj1265	|- ( ph -> ps )

Distinct variable group:   ps, x

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

Proof of Theorem bnj1265

Step	Hyp	Ref	Expression
1		bnj1265.1	. . . 4 |- ( ph -> E. x e. A ps )
2	1	bnj1196 30865	. . 3 |- ( ph -> E. x ( x e. A /\ ps ) )
3	2	bnj1266 30882	. 2 |- ( ph -> E. x ps )
4	3	bnj937 30842	1 |- ( ph -> ps )

Syntax hints:   -> wi 4   e. wcel 1990   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  ax-5 1839  ax-6 1888

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

This theorem is referenced by:  bnj1253  31085  bnj1280  31088  bnj1296  31089  bnj1371  31097  bnj1497  31128