Metamath Proof Explorer

Theorem bj-alalbial

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

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

Proof

Step Hyp Ref Expression
1 nfa1 
 |-  F/ x A. x ph
2 1 19.3 
 |-  ( A. x A. x ph <-> A. x ph )