Theorem bnj534 30808

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

Hypothesis

Ref	Expression
bnj534.1	|- ( ch -> ( E. x ph /\ ps ) )

Assertion

Ref	Expression
bnj534	|- ( ch -> E. x ( ph /\ ps ) )

Distinct variable group:   ps, x

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

Proof of Theorem bnj534

Step	Hyp	Ref	Expression
1		bnj534.1	. 2 |- ( ch -> ( E. x ph /\ ps ) )
2		19.41v 1914	. 2 |- ( E. x ( ph /\ ps ) <-> ( E. x ph /\ ps ) )
3	1, 2	sylibr 224	1 |- ( ch -> E. x ( ph /\ 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  ax-5 1839  ax-6 1888

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

This theorem is referenced by:  bnj600  30989  bnj852  30991