Theorem ferison 2165

Description: "Ferison", one of the syllogisms of Aristotelian logic. No ph is ps, and some ph is ch, therefore some ch is not ps. (In Aristotelian notation, EIO-3: MeP and MiS therefore SoP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)

Hypotheses

Ref	Expression
ferison.maj	|- A. x ( ph -> -. ps )
ferison.min	|- E. x ( ph /\ ch )

Assertion

Ref	Expression
ferison	|- E. x ( ch /\ -. ps )

Proof of Theorem ferison

Step	Hyp	Ref	Expression
1		ferison.maj	. 2 |- A. x ( ph -> -. ps )
2		ferison.min	. 2 |- E. x ( ph /\ ch )
3	1, 2	datisi 2163	1 |- E. x ( ch /\ -. ps )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104   A.wal 1370   E.wex 1514

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-4 1532  ax-ial 1556

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)