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Theorem syl232anc 1255
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
syl232anc.8
Assertion
Ref Expression
syl232anc

Proof of Theorem syl232anc
StepHypRef Expression
1 sylXanc.1 . 2
2 sylXanc.2 . 2
3 sylXanc.3 . 2
4 sylXanc.4 . 2
5 sylXanc.5 . 2
6 sylXanc.6 . . 3
7 sylXanc.7 . . 3
86, 7jca 532 . 2
9 syl232anc.8 . 2
101, 2, 3, 4, 5, 8, 9syl231anc 1248 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  /\w3a 973
This theorem is referenced by:  ax5seg  24241  cdleme20d  36038  cdleme22cN  36068  cdleme27a  36093
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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