Metamath Proof Explorer


Theorem uunTT1

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis uunTT1.1 ( ( ⊤ ∧ ⊤ ∧ 𝜑 ) → 𝜓 )
Assertion uunTT1 ( 𝜑𝜓 )

Proof

Step Hyp Ref Expression
1 uunTT1.1 ( ( ⊤ ∧ ⊤ ∧ 𝜑 ) → 𝜓 )
2 3anass ( ( ⊤ ∧ ⊤ ∧ 𝜑 ) ↔ ( ⊤ ∧ ( ⊤ ∧ 𝜑 ) ) )
3 anabs5 ( ( ⊤ ∧ ( ⊤ ∧ 𝜑 ) ) ↔ ( ⊤ ∧ 𝜑 ) )
4 truan ( ( ⊤ ∧ 𝜑 ) ↔ 𝜑 )
5 2 3 4 3bitri ( ( ⊤ ∧ ⊤ ∧ 𝜑 ) ↔ 𝜑 )
6 5 1 sylbir ( 𝜑𝜓 )