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Theorem syl223anc 1211
 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
syl223anc.8
Assertion
Ref Expression
syl223anc

Proof of Theorem syl223anc
StepHypRef Expression
1 sylXanc.1 . 2
2 sylXanc.2 . 2
3 sylXanc.3 . . 3
4 sylXanc.4 . . 3
53, 4jca 520 . 2
6 sylXanc.5 . 2
7 sylXanc.6 . 2
8 sylXanc.7 . 2
9 syl223anc.8 . 2
101, 2, 5, 6, 7, 8, 9syl213anc 1204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937 This theorem is referenced by:  cdleme17d1  31087  cdlemednpq  31097  cdleme19d  31104  cdleme20aN  31107  cdleme20c  31109  cdleme20f  31112  cdleme20g  31113  cdleme20j  31116  cdleme20l1  31118  cdleme20l2  31119  cdlemky  31724  cdlemkyyN  31760 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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