Metamath Proof Explorer

Theorem bj-alexbiex

Description: Adding a second quantifier over the same variable is a transparent operation, ( A. E. case). (Contributed by BJ, 20-Oct-2019)

Ref Expression
Assertion bj-alexbiex 
|- ( A. x E. x ph <-> E. x ph )

Proof

Step Hyp Ref Expression
1 nfe1 
 |-  F/ x E. x ph
2 1 19.3 
 |-  ( A. x E. x ph <-> E. x ph )