Metamath Proof Explorer


Theorem 3adant3r

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006) (Proof shortened by Wolf Lammen, 25-Jun-2022)

Ref Expression
Hypothesis ad4ant3.1 φ ψ χ θ
Assertion 3adant3r φ ψ χ τ θ

Proof

Step Hyp Ref Expression
1 ad4ant3.1 φ ψ χ θ
2 simpl χ τ χ
3 2 1 syl3an3 φ ψ χ τ θ