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Theorem sylan9 389
Description: Nested syllogism inference conjoining dissimilar antecedents. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Hypotheses
Ref Expression
sylan9.1 (φ → (ψχ))
sylan9.2 (θ → (χτ))
Assertion
Ref Expression
sylan9 ((φ θ) → (ψτ))

Proof of Theorem sylan9
StepHypRef Expression
1 sylan9.1 . . 3 (φ → (ψχ))
2 sylan9.2 . . 3 (θ → (χτ))
31, 2syl9 66 . 2 (φ → (θ → (ψτ)))
43imp 115 1 ((φ θ) → (ψτ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100
This theorem is referenced by:  sbequi  1717  rspc2  2655  rspc3v  2659  trintssm  3861  copsexg  3972  chfnrn  5221  ffnfv  5266  f1elima  5355  smoel2  5859  th3q  6147  addnnnq0  6432  mulnnnq0  6433  addsrpr  6673  mulsrpr  6674
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