Theorem bnj1019

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

	Ref	Expression
Assertion	bnj1019	|- ( E. p ( th /\ ch /\ ta /\ et ) <-> ( th /\ ch /\ et /\ E. p ta ) )

Proof

Step	Hyp	Ref	Expression
1		19.42v	|- ( E. p ( ( th /\ ch /\ et ) /\ ta ) <-> ( ( th /\ ch /\ et ) /\ E. p ta ) )
2		bnj258	|- ( ( th /\ ch /\ ta /\ et ) <-> ( ( th /\ ch /\ et ) /\ ta ) )
3	2	exbii	|- ( E. p ( th /\ ch /\ ta /\ et ) <-> E. p ( ( th /\ ch /\ et ) /\ ta ) )
4		df-bnj17	|- ( ( th /\ ch /\ et /\ E. p ta ) <-> ( ( th /\ ch /\ et ) /\ E. p ta ) )
5	1 3 4	3bitr4i	|- ( E. p ( th /\ ch /\ ta /\ et ) <-> ( th /\ ch /\ et /\ E. p ta ) )