NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  bamalip Unicode version

Theorem bamalip 2324
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 2305. (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 . . . . . 6
32spi 1753 . . . . 5
4 bamalip.min . . . . . 6
54spi 1753 . . . . 5
63, 5syl 15 . . . 4
76ancri 535 . . 3
87eximi 1576 . 2
91, 8ax-mp 5 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wa 358  wal 1540  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator