Theorem uunT12p1

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	uunT12p1.1	⊢ ( ( ⊤ ∧ 𝜓 ∧ 𝜑 ) → 𝜒 )
Assertion	uunT12p1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		uunT12p1.1	⊢ ( ( ⊤ ∧ 𝜓 ∧ 𝜑 ) → 𝜒 )
2		3anass	⊢ ( ( ⊤ ∧ 𝜓 ∧ 𝜑 ) ↔ ( ⊤ ∧ ( 𝜓 ∧ 𝜑 ) ) )
3		truan	⊢ ( ( ⊤ ∧ ( 𝜓 ∧ 𝜑 ) ) ↔ ( 𝜓 ∧ 𝜑 ) )
4	2 3	bitri	⊢ ( ( ⊤ ∧ 𝜓 ∧ 𝜑 ) ↔ ( 𝜓 ∧ 𝜑 ) )
5		ancom	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜓 ∧ 𝜑 ) )
6	4 5	bitr4i	⊢ ( ( ⊤ ∧ 𝜓 ∧ 𝜑 ) ↔ ( 𝜑 ∧ 𝜓 ) )
7	6 1	sylbir	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )