Metamath Proof Explorer


Theorem 3adantl1

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005)

Ref Expression
Hypothesis 3adantl.1 φ ψ χ θ
Assertion 3adantl1 τ φ ψ χ θ

Proof

Step Hyp Ref Expression
1 3adantl.1 φ ψ χ θ
2 3simpc τ φ ψ φ ψ
3 2 1 sylan τ φ ψ χ θ