NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  syl311anc Unicode version

Theorem syl311anc 1196
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
Hypotheses
Ref Expression
sylXanc.1
sylXanc.2
sylXanc.3
sylXanc.4
sylXanc.5
syl311anc.6
Assertion
Ref Expression
syl311anc

Proof of Theorem syl311anc
StepHypRef Expression
1 sylXanc.1 . . 3
2 sylXanc.2 . . 3
3 sylXanc.3 . . 3
41, 2, 33jca 1132 . 2
5 sylXanc.4 . 2
6 sylXanc.5 . 2
7 syl311anc.6 . 2
84, 5, 6, 7syl3anc 1182 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  syl312anc  1203  syl321anc  1204  syl313anc  1206  syl331anc  1207
  Copyright terms: Public domain W3C validator