Metamath Proof Explorer

Theorem bj-exalbial

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

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

Proof

Step Hyp Ref Expression
1 nfa1 
 |-  F/ x A. x ph
2 1 19.9 
 |-  ( E. x A. x ph <-> A. x ph )