Metamath Proof Explorer


Theorem exnalimn

Description: Existential quantification of a conjunction expressed with only primitive symbols ( -> , -. , A. ). (Contributed by NM, 10-May-1993) State the most general instance. (Revised by BJ, 29-Sep-2019)

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

Proof

Step Hyp Ref Expression
1 alinexa
 |-  ( A. x ( ph -> -. ps ) <-> -. E. x ( ph /\ ps ) )
2 1 con2bii
 |-  ( E. x ( ph /\ ps ) <-> -. A. x ( ph -> -. ps ) )