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Metamath Proof Explorer

Theorem adantlrr

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004) (Proof shortened by Wolf Lammen, 4-Dec-2012)

Ref Expression
Hypothesis adantl2.1 ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
Assertion adantlrr ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜏 ) ) ∧ 𝜒 ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 adantl2.1 ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
2 simpl ⊢ ( ( 𝜓 ∧ 𝜏 ) → 𝜓 )
3 2 1 sylanl2 ⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜏 ) ) ∧ 𝜒 ) → 𝜃 )