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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
StepHypRef Expression
1 bamalip.e . 2
2 bamalip.maj . . . . 5
32spi 1864 . . . 4
4 bamalip.min . . . . 5
54spi 1864 . . . 4
63, 5syl 16 . . 3
76ancri 552 . 2
81, 7eximii 1658 1
 Colors of variables: wff setvar class 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
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