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Theorem syl6ci 71
Description: A syllogism inference combined with contraction. (Contributed by Alan Sare, 18-Mar-2012.)
Hypotheses
Ref Expression
syl6ci.1 (𝜑 → (𝜓𝜒))
syl6ci.2 (𝜑𝜃)
syl6ci.3 (𝜒 → (𝜃𝜏))
Assertion
Ref Expression
syl6ci (𝜑 → (𝜓𝜏))

Proof of Theorem syl6ci
StepHypRef Expression
1 syl6ci.1 . 2 (𝜑 → (𝜓𝜒))
2 syl6ci.2 . . 3 (𝜑𝜃)
32a1d 25 . 2 (𝜑 → (𝜓𝜃))
4 syl6ci.3 . 2 (𝜒 → (𝜃𝜏))
51, 3, 4syl6c 70 1 (𝜑 → (𝜓𝜏))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  mtord  879  reu6  3723  axprlem3  5424  ordelord  6387  f1dmex  7943  soseq  8145  omeulem2  8583  2pwuninel  9132  isumrpcl  15789  kqfvima  23234  caubl  24825  nbupgr  28601  nbumgrvtx  28603  umgr2adedgspth  29202  btwnconn1lem12  35070  omabs2  42082  sbcim2g  43299  ee21an  43493
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