This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem uun132

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	uun132.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
	Assertion	uun132	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		uun132.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
2		3anass	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) )
3	2 1	sylbi	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )