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Metamath Proof Explorer

Theorem ee4anvOLD

Description: Obsolete version of ee4anv as of 26-Oct-2025. (Contributed by NM, 31-Jul-1995) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion ee4anvOLD 
|- ( E. x E. y E. z E. w ( ph /\ ps ) <-> ( E. x E. y ph /\ E. z E. w ps ) )

Proof

Step Hyp Ref Expression
1 excom 
 |-  ( E. y E. z E. w ( ph /\ ps ) <-> E. z E. y E. w ( ph /\ ps ) )
2 1 exbii 
 |-  ( E. x E. y E. z E. w ( ph /\ ps ) <-> E. x E. z E. y E. w ( ph /\ ps ) )
3 eeanv 
 |-  ( E. y E. w ( ph /\ ps ) <-> ( E. y ph /\ E. w ps ) )
4 3 2exbii 
 |-  ( E. x E. z E. y E. w ( ph /\ ps ) <-> E. x E. z ( E. y ph /\ E. w ps ) )
5 eeanv 
 |-  ( E. x E. z ( E. y ph /\ E. w ps ) <-> ( E. x E. y ph /\ E. z E. w ps ) )
6 2 4 5 3bitri 
 |-  ( E. x E. y E. z E. w ( ph /\ ps ) <-> ( E. x E. y ph /\ E. z E. w ps ) )