Theorem uun132p1

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	uun132p1.1	⊢ ( ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜑 ) → 𝜃 )
Assertion	uun132p1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		uun132p1.1	⊢ ( ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜑 ) → 𝜃 )
2		3anass	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) )
3		ancom	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) ↔ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜑 ) )
4	2 3	bitri	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜑 ) )
5	4 1	sylbi	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )