Metamath Proof Explorer


Theorem 3adantr3

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005)

Ref Expression
Hypothesis 3adantr.1 φ ψ χ θ
Assertion 3adantr3 φ ψ χ τ θ

Proof

Step Hyp Ref Expression
1 3adantr.1 φ ψ χ θ
2 3simpa ψ χ τ ψ χ
3 2 1 sylan2 φ ψ χ τ θ