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Theorem syli 33
Description: Syllogism inference with common nested antecedent. (Contributed by NM, 4-Nov-2004.)
Hypotheses
Ref Expression
syli.1 (ψ → (φχ))
syli.2 (χ → (φθ))
Assertion
Ref Expression
syli (ψ → (φθ))

Proof of Theorem syli
StepHypRef Expression
1 syli.1 . 2 (ψ → (φχ))
2 syli.2 . . 3 (χ → (φθ))
32com12 27 . 2 (φ → (χθ))
41, 3sylcom 25 1 (ψ → (φθ))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  ibd  167  bijadc  775  sbi2v  1769  elab3gf  2686  elreldm  4503  tz6.12c  5146  rntpos  5813  smores  5848  f1domg  6174  negm  8326
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