Theorem adantrrr 705

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
adantrrr	⊢ ((φ ∧ (ψ ∧ (χ ∧ τ))) → θ)

Proof of Theorem adantrrr

Step	Hyp	Ref	Expression
1		simpl 443	. 2 ⊢ ((χ ∧ τ) → χ)
2		adantr2.1	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
3	1, 2	sylanr2 634	1 ⊢ ((φ ∧ (ψ ∧ (χ ∧ τ))) → 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)