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Theorem 3anandirs 1223
 Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 25-Jul-2006.) (Revised by NM, 18-Apr-2007.)
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 895 . 2 (((φ ψ χ) θ) → φ)
2 simpr 103 . 2 (((φ ψ χ) θ) → θ)
3 simpl2 896 . 2 (((φ ψ χ) θ) → ψ)
4 simpl3 897 . 2 (((φ ψ χ) θ) → χ)
5 3anandirs.1 . 2 (((φ θ) (ψ θ) (χ θ)) → τ)
61, 2, 3, 2, 4, 2, 5syl222anc 1137 1 (((φ ψ χ) θ) → τ)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∧ w3a 873 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101 This theorem depends on definitions:  df-bi 110  df-3an 875 This theorem is referenced by: (None)
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