Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  bamalip Unicode version

Theorem bamalip 2263
 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 2244. (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 1738 . . . . 5
4 bamalip.min . . . . . 6
54spi 1738 . . . . 5
63, 5syl 15 . . . 4
76ancri 535 . . 3
87eximi 1563 . 2
91, 8ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wal 1527  wex 1528 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
 Copyright terms: Public domain W3C validator