Metamath Proof Explorer

Theorem exintrbi

Description: Add/remove a conjunct in the scope of an existential quantifier. (Contributed by Raph Levien, 3-Jul-2006)

Ref Expression
Assertion exintrbi 
|- ( A. x ( ph -> ps ) -> ( E. x ph <-> E. x ( ph /\ ps ) ) )

Proof

Step Hyp Ref Expression
1 abai 
 |-  ( ( ph /\ ps ) <-> ( ph /\ ( ph -> ps ) ) )
2 1 rbaibr 
 |-  ( ( ph -> ps ) -> ( ph <-> ( ph /\ ps ) ) )
3 2 alexbii 
 |-  ( A. x ( ph -> ps ) -> ( E. x ph <-> E. x ( ph /\ ps ) ) )