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Theorem syl31anc 1137
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
Hypotheses
Ref Expression
sylXanc.1
sylXanc.2
sylXanc.3
sylXanc.4
syl31anc.5
Assertion
Ref Expression
syl31anc

Proof of Theorem syl31anc
StepHypRef Expression
1 sylXanc.1 . . 3
2 sylXanc.2 . . 3
3 sylXanc.3 . . 3
41, 2, 33jca 1083 . 2
5 sylXanc.4 . 2
6 syl31anc.5 . 2
74, 5, 6syl2anc 391 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   w3a 884
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 886
This theorem is referenced by:  syl32anc  1142  stoic4b  1319  enq0tr  6416  ltmul12a  7587  lt2msq1  7612  ledivp1  7630  lemul1ad  7666  lemul2ad  7667  lediv2ad  8399  difelfznle  8743  expubnd  8945
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