This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pm2.61ddan

Description: Elimination of two antecedents. (Contributed by NM, 9-Jul-2013)

Ref Expression
Hypotheses pm2.61ddan.1 ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )
pm2.61ddan.2 ⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
pm2.61ddan.3 ⊢ ( ( 𝜑 ∧ ( ¬ 𝜓 ∧ ¬ 𝜒 ) ) → 𝜃 )
Assertion pm2.61ddan ( 𝜑 → 𝜃 )

Proof

Step Hyp Ref Expression
1 pm2.61ddan.1 ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )
2 pm2.61ddan.2 ⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
3 pm2.61ddan.3 ⊢ ( ( 𝜑 ∧ ( ¬ 𝜓 ∧ ¬ 𝜒 ) ) → 𝜃 )
4 2 adantlr ⊢ ( ( ( 𝜑 ∧ ¬ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
5 3 anassrs ⊢ ( ( ( 𝜑 ∧ ¬ 𝜓 ) ∧ ¬ 𝜒 ) → 𝜃 )
6 4 5 pm2.61dan ⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) → 𝜃 )
7 1 6 pm2.61dan ⊢ ( 𝜑 → 𝜃 )