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Metamath Proof Explorer

Theorem bnj1254

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Hypothesis bnj1254.1 ⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏 ) )
Assertion bnj1254 ( 𝜑 → 𝜏 )

Proof

Step Hyp Ref Expression
1 bnj1254.1 ⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏 ) )
2 id ⊢ ( 𝜏 → 𝜏 )
3 2 bnj708 ⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏 ) → 𝜏 )
4 1 3 sylbi ⊢ ( 𝜑 → 𝜏 )