Theorem adantlll 698

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 2-Dec-2012.)

Hypothesis

Ref	Expression
adantl2.1	⊢ (((φ ∧ ψ) ∧ χ) → θ)

Assertion

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

Proof of Theorem adantlll

Step	Hyp	Ref	Expression
1		simpr 447	. 2 ⊢ ((τ ∧ φ) → φ)
2		adantl2.1	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
3	1, 2	sylanl1 631	1 ⊢ ((((τ ∧ φ) ∧ ψ) ∧ χ) → θ)

Syntax hints:   → wi 4   ∧ wa 358

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

This theorem is referenced by: (None)