Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  bamalip Unicode version

Theorem bamalip 2064
 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 2045. (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 1470 . . . 4
4 bamalip.min . . . . 5
54spi 1470 . . . 4
63, 5syl 14 . . 3
76ancri 317 . 2
81, 7eximii 1534 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102  wal 1283  wex 1422 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468 This theorem depends on definitions:  df-bi 115 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator