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Metamath Proof Explorer

Theorem pm2.61dan

Description: Elimination of an antecedent. (Contributed by NM, 1-Jan-2005)

Ref Expression
Hypotheses pm2.61dan.1 ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
pm2.61dan.2 ⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) → 𝜒 )
Assertion pm2.61dan ( 𝜑 → 𝜒 )

Proof

Step Hyp Ref Expression
1 pm2.61dan.1 ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2 pm2.61dan.2 ⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) → 𝜒 )
3 1 ex ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4 2 ex ⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
5 3 4 pm2.61d ⊢ ( 𝜑 → 𝜒 )