Metamath Proof Explorer


Theorem 3adant1r

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006) (Proof shortened by Wolf Lammen, 23-Jun-2022)

Ref Expression
Hypothesis ad4ant3.1 φ ψ χ θ
Assertion 3adant1r φ τ ψ χ θ

Proof

Step Hyp Ref Expression
1 ad4ant3.1 φ ψ χ θ
2 simpl φ τ φ
3 2 1 syl3an1 φ τ ψ χ θ