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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  1681  cbvexdh  1801  repizf2  3915  issref  4707  fnun  5005  ovigg  5621  tfrlem9  5935  tfri3  5953  ordge1n0im  6019  nntri3or  6072  axprecex  6954  peano5nnnn  6966  peano5nni  7917  zeo  8343  nn0ind-raph  8355  fzm1  8962  fzind2  9095  fzfig  9206  climrecvg1n  9867  bj-intabssel  9928
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