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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  1657  cbvexdh  1777  repizf2  3881  issref  4625  fnun  4922  ovigg  5535  tfrlem9  5848  tfri3  5866  ordge1n0im  5925  nntri3or  5978  axprecex  6572  peano5nni  7503  zeo  7911  nn0ind-raph  7923  bj-intabssel  8385
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