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Theorem syl313anc 1252
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
Hypotheses
Ref Expression
sylXanc.1
sylXanc.2
sylXanc.3
sylXanc.4
sylXanc.5
sylXanc.6
sylXanc.7
syl313anc.8
Assertion
Ref Expression
syl313anc

Proof of Theorem syl313anc
StepHypRef Expression
1 sylXanc.1 . 2
2 sylXanc.2 . 2
3 sylXanc.3 . 2
4 sylXanc.4 . 2
5 sylXanc.5 . . 3
6 sylXanc.6 . . 3
7 sylXanc.7 . . 3
85, 6, 73jca 1176 . 2
9 syl313anc.8 . 2
101, 2, 3, 4, 8, 9syl311anc 1242 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\w3a 973
This theorem is referenced by:  syl323anc  1258  osumcllem6N  35685  cdlemg13  36378  cdlemk7u  36596  cdlemk31  36622  cdlemk27-3  36633  cdlemk19ylem  36656  cdlemk46  36674
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  df-3an 975
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