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Metamath Proof Explorer

Theorem mpanr1

Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994) (Proof shortened by Andrew Salmon, 7-May-2011)

Ref Expression
Hypotheses mpanr1.1 ⊢ 𝜓
mpanr1.2 ⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
Assertion mpanr1 ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 mpanr1.1 ⊢ 𝜓
2 mpanr1.2 ⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
3 2 anassrs ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
4 1 3 mpanl2 ⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )