Theorem imp44 289

Description: An importation inference.

Hypothesis

Ref	Expression
imp4.1	⊢ (φ → (ψ → (χ → (θ → τ))))

Assertion

Ref	Expression
imp44	⊢ ((φ ∧ ((ψ ∧ χ) ∧ θ)) → τ)

Proof of Theorem imp44

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → τ))))
2	1	imp4c 284	. 2 ⊢ (φ → (((ψ ∧ χ) ∧ θ) → τ))
3	2	imp 277	1 ⊢ ((φ ∧ ((ψ ∧ χ) ∧ θ)) → τ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  adantrll 316  adantrlr 317  mdsymlem4 5779  mdsymlem5 5780

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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