Theorem adantrll 316

Description: Deduction adding a conjunct to an antecedent.

Hypothesis

Ref	Expression
adantr2.1	⊢ ((φ ∧ (ψ ∧ χ)) → θ)

Assertion

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

Proof of Theorem adantrll

Step	Hyp	Ref	Expression
1		adantr2.1	. . . 4 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
2	1	exp32 294	. . 3 ⊢ (φ → (ψ → (χ → θ)))
3	2	a1d 14	. 2 ⊢ (φ → (τ → (ψ → (χ → θ))))
4	3	imp44 289	1 ⊢ ((φ ∧ ((τ ∧ ψ) ∧ χ)) → θ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  distrlem4pr 3924

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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