Theorem uunTT1p1

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	uunTT1p1.1	⊢ ( ( ⊤ ∧ 𝜑 ∧ ⊤ ) → 𝜓 )
Assertion	uunTT1p1	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		uunTT1p1.1	⊢ ( ( ⊤ ∧ 𝜑 ∧ ⊤ ) → 𝜓 )
2		3ancomb	⊢ ( ( ⊤ ∧ 𝜑 ∧ ⊤ ) ↔ ( ⊤ ∧ ⊤ ∧ 𝜑 ) )
3		3anass	⊢ ( ( ⊤ ∧ ⊤ ∧ 𝜑 ) ↔ ( ⊤ ∧ ( ⊤ ∧ 𝜑 ) ) )
4		anabs5	⊢ ( ( ⊤ ∧ ( ⊤ ∧ 𝜑 ) ) ↔ ( ⊤ ∧ 𝜑 ) )
5	2 3 4	3bitri	⊢ ( ( ⊤ ∧ 𝜑 ∧ ⊤ ) ↔ ( ⊤ ∧ 𝜑 ) )
6		truan	⊢ ( ( ⊤ ∧ 𝜑 ) ↔ 𝜑 )
7	5 6	bitri	⊢ ( ( ⊤ ∧ 𝜑 ∧ ⊤ ) ↔ 𝜑 )
8	7 1	sylbir	⊢ ( 𝜑 → 𝜓 )