Theorem bnj132 30792

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) (New usage is discouraged.)

Hypothesis

Ref	Expression
bnj132.1	|- ( ph <-> E. x ( ps -> ch ) )

Assertion

Ref	Expression
bnj132	|- ( ph <-> ( ps -> E. x ch ) )

Distinct variable group:   ps, x

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

Proof of Theorem bnj132

Step	Hyp	Ref	Expression
1		bnj132.1	. 2 |- ( ph <-> E. x ( ps -> ch ) )
2		19.37v 1910	. 2 |- ( E. x ( ps -> ch ) <-> ( ps -> E. x ch ) )
3	1, 2	bitri 264	1 |- ( ph <-> ( ps -> E. x ch ) )

Syntax hints:   -> wi 4   <-> wb 196   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  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  bnj996  31025