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Theorem 3anandis 1283
Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 18-Apr-2007.)
Hypothesis
Ref Expression
3anandis.1 (((φ ψ) (φ χ) (φ θ)) → τ)
Assertion
Ref Expression
3anandis ((φ (ψ χ θ)) → τ)

Proof of Theorem 3anandis
StepHypRef Expression
1 simpl 443 . 2 ((φ (ψ χ θ)) → φ)
2 simpr1 961 . 2 ((φ (ψ χ θ)) → ψ)
3 simpr2 962 . 2 ((φ (ψ χ θ)) → χ)
4 simpr3 963 . 2 ((φ (ψ χ θ)) → θ)
5 3anandis.1 . 2 (((φ ψ) (φ χ) (φ θ)) → τ)
61, 2, 1, 3, 1, 4, 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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