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Metamath Proof Explorer

Theorem bnj769

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

Ref Expression
Hypotheses bnj769.1 ⊢ ( 𝜂 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) )
bnj769.2 ⊢ ( 𝜑 → 𝜏 )
Assertion bnj769 ( 𝜂 → 𝜏 )

Proof

Step Hyp Ref Expression
1 bnj769.1 ⊢ ( 𝜂 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) )
2 bnj769.2 ⊢ ( 𝜑 → 𝜏 )
3 2 bnj705 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 )
4 1 3 sylbi ⊢ ( 𝜂 → 𝜏 )