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Metamath Proof Explorer

Theorem 3adant3r

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006) (Proof shortened by Wolf Lammen, 25-Jun-2022)

Ref Expression
Hypothesis ad4ant3.1 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion 3adant3r ( ( 𝜑 ∧ 𝜓 ∧ ( 𝜒 ∧ 𝜏 ) ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 ad4ant3.1 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
2 simpl ⊢ ( ( 𝜒 ∧ 𝜏 ) → 𝜒 )
3 2 1 syl3an3 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ ( 𝜒 ∧ 𝜏 ) ) → 𝜃 )