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Theorem 3anandirs 1284
Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 25-Jul-2006.)
Hypothesis
Ref Expression
3anandirs.1 (((φ θ) (ψ θ) (χ θ)) → τ)
Assertion
Ref Expression
3anandirs (((φ ψ χ) θ) → τ)

Proof of Theorem 3anandirs
StepHypRef Expression
1 simpl1 958 . 2 (((φ ψ χ) θ) → φ)
2 simpr 447 . 2 (((φ ψ χ) θ) → θ)
3 simpl2 959 . 2 (((φ ψ χ) θ) → ψ)
4 simpl3 960 . 2 (((φ ψ χ) θ) → χ)
5 3anandirs.1 . 2 (((φ θ) (ψ θ) (χ θ)) → τ)
61, 2, 3, 2, 4, 2, 5syl222anc 1198 1 (((φ ψ χ) θ) → τ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   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: (None)
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