Metamath Proof Explorer


Theorem ecase3ad

Description: Deduction for elimination by cases. (Contributed by NM, 24-May-2013) (Proof shortened by Wolf Lammen, 20-Sep-2024)

Ref Expression
Hypotheses ecase3ad.1 φψθ
ecase3ad.2 φχθ
ecase3ad.3 φ¬ψ¬χθ
Assertion ecase3ad φθ

Proof

Step Hyp Ref Expression
1 ecase3ad.1 φψθ
2 ecase3ad.2 φχθ
3 ecase3ad.3 φ¬ψ¬χθ
4 1 imp φψθ
5 2 imp φχθ
6 3 imp φ¬ψ¬χθ
7 4 5 6 pm2.61ddan φθ