Metamath Proof Explorer

Theorem exinst01

Description: Existential Instantiation. Virtual Deduction rule corresponding to a special case of the Natural Deduction Sequent Calculus rule called Rule C in Margaris p. 79 and E E. in Table 1 on page 4 of the paper "Extracting information from intermediate T-systems" (2000) presented at IMLA99 by Mauro Ferrari, Camillo Fiorentini, and Pierangelo Miglioli. (Contributed by Alan Sare, 21-Apr-2013) (Proof modification is discouraged.) (New usage is discouraged.)

|- E. x ps

|- (. ph ,. ps ->. ch ).

|- ( ph -> A. x ph )

|- ( ch -> A. x ch )

|- (. ph ->. ch ).

 |-  E. x ps

 |-  (. ph ,. ps ->. ch ).

 |-  ( ph -> A. x ph )

 |-  ( ch -> A. x ch )

 |-  ( ph -> ( ps -> ch ) )

 |-  ( ph -> ch )

 |-  (. ph ->. ch ).