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Theorem syl9 66
Description: A nested syllogism inference with different antecedents. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.)
Hypotheses
Ref Expression
syl9.1 (φ → (ψχ))
syl9.2 (θ → (χτ))
Assertion
Ref Expression
syl9 (φ → (θ → (ψτ)))

Proof of Theorem syl9
StepHypRef Expression
1 syl9.1 . 2 (φ → (ψχ))
2 syl9.2 . . 3 (θ → (χτ))
32a1i 10 . 2 (φ → (θ → (χτ)))
41, 3syl5d 62 1 (φ → (θ → (ψτ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  syl9r  67  com23  72  sylan9  638  19.21t  1795  19.21tOLD  1863  sbequi  2059  sbal1  2126  reuss2  3535  reupick  3539  ssfin  4470  iss  5000
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