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Metamath Proof Explorer

Theorem mpanlr1

Description: An inference based on modus ponens. (Contributed by NM, 30-Dec-2004) (Proof shortened by Wolf Lammen, 7-Apr-2013)

Ref Expression
Hypotheses mpanlr1.1 ⊢ ψ
mpanlr1.2 ⊢ φ ∧ ψ ∧ χ ∧ θ → τ
Assertion mpanlr1 ⊢ φ ∧ χ ∧ θ → τ

Proof

Step Hyp Ref Expression
1 mpanlr1.1 ⊢ ψ
2 mpanlr1.2 ⊢ φ ∧ ψ ∧ χ ∧ θ → τ
3 1 jctl ⊢ χ → ψ ∧ χ
4 3 2 sylanl2 ⊢ φ ∧ χ ∧ θ → τ