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Metamath Proof Explorer

Theorem bnj837

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Hypotheses bnj837.1 ⊢ ( 𝜂 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )
bnj837.2 ⊢ ( 𝜒 → 𝜏 )
Assertion bnj837 ( 𝜂 → 𝜏 )

Proof

Step Hyp Ref Expression
1 bnj837.1 ⊢ ( 𝜂 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )
2 bnj837.2 ⊢ ( 𝜒 → 𝜏 )
3 2 3ad2ant3 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜏 )
4 1 3 sylbi ⊢ ( 𝜂 → 𝜏 )