Metamath Proof Explorer


Theorem adantrrr

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

Ref Expression
Hypothesis adantr2.1 φ ψ χ θ
Assertion adantrrr φ ψ χ τ θ

Proof

Step Hyp Ref Expression
1 adantr2.1 φ ψ χ θ
2 simpl χ τ χ
3 2 1 sylanr2 φ ψ χ τ θ