Theorem uun111

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	uun111.1	⊢ ( ( 𝜑 ∧ 𝜑 ∧ 𝜑 ) → 𝜓 )
Assertion	uun111	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		uun111.1	⊢ ( ( 𝜑 ∧ 𝜑 ∧ 𝜑 ) → 𝜓 )
2		3anass	⊢ ( ( 𝜑 ∧ 𝜑 ∧ 𝜑 ) ↔ ( 𝜑 ∧ ( 𝜑 ∧ 𝜑 ) ) )
3		anabs5	⊢ ( ( 𝜑 ∧ ( 𝜑 ∧ 𝜑 ) ) ↔ ( 𝜑 ∧ 𝜑 ) )
4		anidm	⊢ ( ( 𝜑 ∧ 𝜑 ) ↔ 𝜑 )
5	2 3 4	3bitri	⊢ ( ( 𝜑 ∧ 𝜑 ∧ 𝜑 ) ↔ 𝜑 )
6	5 1	sylbir	⊢ ( 𝜑 → 𝜓 )