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Theorem syl221anc 1228
 Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
Hypotheses
Ref Expression
sylXanc.1
sylXanc.2
sylXanc.3
sylXanc.4
sylXanc.5
syl221anc.6
Assertion
Ref Expression
syl221anc

Proof of Theorem syl221anc
StepHypRef Expression
1 sylXanc.1 . 2
2 sylXanc.2 . 2
3 sylXanc.3 . . 3
4 sylXanc.4 . . 3
53, 4jca 304 . 2
6 sylXanc.5 . 2
7 syl221anc.6 . 2
81, 2, 5, 6, 7syl211anc 1223 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   w3a 963 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107 This theorem depends on definitions:  df-bi 116  df-3an 965 This theorem is referenced by:  syl222anc  1233  vtocldf  2740  dmdcanapd  8603  exprecap  10364  xrbdtri  11076  2strbasg  12097  2stropg  12098  cnptoprest  12445  blssps  12633  blss  12634  metequiv2  12702  xmettx  12716
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