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Theorem syl6bir 153
Description: A mixed syllogism inference. (Contributed by NM, 18-May-1994.)
Hypotheses
Ref Expression
syl6bir.1 (φ → (χψ))
syl6bir.2 (χθ)
Assertion
Ref Expression
syl6bir (φ → (ψθ))

Proof of Theorem syl6bir
StepHypRef Expression
1 syl6bir.1 . . 3 (φ → (χψ))
21biimprd 147 . 2 (φ → (ψχ))
3 syl6bir.2 . 2 (χθ)
42, 3syl6 29 1 (φ → (ψθ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
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
This theorem is referenced by:  exdistrfor  1678  cbvexdh  1798  repizf2  3906  issref  4650  fnun  4948  ovigg  5563  tfrlem9  5876  tfri3  5894  ordge1n0im  5958  nntri3or  6011  axprecex  6744  peano5nni  7678  zeo  8099  nn0ind-raph  8111  fzm1  8712  fzind2  8845  fzfig  8867  bj-intabssel  9243
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