Theorem uun123

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	uun123.1	⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜓 ) → 𝜃 )
Assertion	uun123	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		uun123.1	⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜓 ) → 𝜃 )
2		3ancomb	⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜓 ) ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )
3	2 1	sylbir	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )