Theorem bamalip 2419

Description: "Bamalip", one of the syllogisms of Aristotelian logic. All is , all is , and exist, therefore some is . (In Aristotelian notation, AAI-4: PaM and MaS therefore SiP.) Like barbari 2400. (Contributed by David A. Wheeler, 28-Aug-2016.)

Hypotheses

Ref	Expression
bamalip.maj
bamalip.min
bamalip.e

Assertion

Ref	Expression
bamalip

Proof of Theorem bamalip

Step	Hyp	Ref	Expression
1		bamalip.e	. 2
2		bamalip.maj	. . . . 5
3	2	spi 1864	. . . 4
4		bamalip.min	. . . . 5
5	4	spi 1864	. . . 4
6	3, 5	syl 16	. . 3
7	6	ancri 552	. 2
8	1, 7	eximii 1658	1

Syntax hints:  ->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