Metamath Proof Explorer


Theorem adantlrl

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004) (Proof shortened by Wolf Lammen, 4-Dec-2012)

Ref Expression
Hypothesis adantl2.1 φ ψ χ θ
Assertion adantlrl φ τ ψ χ θ

Proof

Step Hyp Ref Expression
1 adantl2.1 φ ψ χ θ
2 simpr τ ψ ψ
3 2 1 sylanl2 φ τ ψ χ θ