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Theorem syl3an9b 1250
Description: Nested syllogism inference conjoining 3 dissimilar antecedents. (Contributed by NM, 1-May-1995.)
Hypotheses
Ref Expression
syl3an9b.1 (φ → (ψχ))
syl3an9b.2 (θ → (χτ))
syl3an9b.3 (η → (τζ))
Assertion
Ref Expression
syl3an9b ((φ θ η) → (ψζ))

Proof of Theorem syl3an9b
StepHypRef Expression
1 syl3an9b.1 . . . 4 (φ → (ψχ))
2 syl3an9b.2 . . . 4 (θ → (χτ))
31, 2sylan9bb 680 . . 3 ((φ θ) → (ψτ))
4 syl3an9b.3 . . 3 (η → (τζ))
53, 4sylan9bb 680 . 2 (((φ θ) η) → (ψζ))
653impa 1146 1 ((φ θ η) → (ψζ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  eloprabg  5579
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