Metamath Proof Explorer


Theorem 3adant1l

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 3adant1l τ φ ψ χ θ

Proof

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