Theorem adantrll 702

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)

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		simpr 447	. 2 ⊢ ((τ ∧ ψ) → ψ)
2		adantr2.1	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
3	1, 2	sylanr1 633	1 ⊢ ((φ ∧ ((τ ∧ ψ) ∧ χ)) → θ)

This proof depends on syntax axioms:   → wi 4   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)