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Theorem sylancb 665
Description: A syllogism inference combined with contraction. (Contributed by NM, 3-Sep-2004.)
Hypotheses
Ref Expression
sylancb.1
sylancb.2
sylancb.3
Assertion
Ref Expression
sylancb

Proof of Theorem sylancb
StepHypRef Expression
1 sylancb.1 . . 3
2 sylancb.2 . . 3
3 sylancb.3 . . 3
41, 2, 3syl2anb 479 . 2
54anidms 645 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369
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 185  df-an 371
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