Theorem bnj1266 30882

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

Hypothesis

Ref	Expression
bnj1266.1	|- ( ch -> E. x ( ph /\ ps ) )

Assertion

Ref	Expression
bnj1266	|- ( ch -> E. x ps )

Proof of Theorem bnj1266

Step	Hyp	Ref	Expression
1		bnj1266.1	. 2 |- ( ch -> E. x ( ph /\ ps ) )
2		simpr 477	. 2 |- ( ( ph /\ ps ) -> ps )
3	1, 2	bnj593 30815	1 |- ( ch -> E. x ps )

Syntax hints:   -> wi 4   /\ wa 384   E.wex 1704

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

This theorem is referenced by:  bnj1265  30883