Theorem uun121p1

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	uun121p1.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜑 ) → 𝜒 )
Assertion	uun121p1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		uun121p1.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜑 ) → 𝜒 )
2		anabs1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜑 ) ↔ ( 𝜑 ∧ 𝜓 ) )
3	2 1	sylbir	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )