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Theorem syl232anc 1212
 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 520 . 2
9 syl232anc.8 . 2
101, 2, 3, 4, 5, 8, 9syl231anc 1205 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937 This theorem is referenced by:  ax5seg  25879  cdleme20d  31111  cdleme22cN  31141  cdleme27a  31166 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 179  df-an 362  df-3an 939
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