Theorem fresison 2416

Description: "Fresison", one of the syllogisms of Aristotelian logic. No is (PeM), and some is (MiS), therefore some is not (SoP). (In Aristotelian notation, EIO-4: PeM and MiS therefore SoP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)

Hypotheses

Ref	Expression
fresison.maj
fresison.min

Assertion

Ref	Expression
fresison

Proof of Theorem fresison

Step	Hyp	Ref	Expression
1		fresison.min	. 2
2		simpr 461	. . 3
3		fresison.maj	. . . . . 6
4	3	spi 1864	. . . . 5
5	4	con2i 120	. . . 4
6	5	adantr 465	. . 3
7	2, 6	jca 532	. 2
8	1, 7	eximii 1658	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613