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

Theorem syldan 456
Description: A syllogism deduction with conjoined antecedents. (Contributed by NM, 24-Feb-2005.) (Proof shortened by Wolf Lammen, 6-Apr-2013.)
Hypotheses
Ref Expression
syldan.1
syldan.2
Assertion
Ref Expression
syldan

Proof of Theorem syldan
StepHypRef Expression
1 syldan.1 . 2
2 syldan.2 . . . 4
32expcom 424 . . 3
43adantrd 454 . 2
51, 4mpcom 32 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  sylan2  460  sbcied2  3083  csbied2  3179  lefinaddc  4450  vfinncvntsp  4549  addlec  6208  nchoicelem5  6293
  Copyright terms: Public domain W3C validator