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Metamath Proof Explorer

Theorem uunT1p1

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	uunT1p1.1	⊢ ( ( 𝜑 ∧ ⊤ ) → 𝜓 )
	Assertion	uunT1p1	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		uunT1p1.1	⊢ ( ( 𝜑 ∧ ⊤ ) → 𝜓 )
2		ancom	⊢ ( ( 𝜑 ∧ ⊤ ) ↔ ( ⊤ ∧ 𝜑 ) )
3		truan	⊢ ( ( ⊤ ∧ 𝜑 ) ↔ 𝜑 )
4	2 3	bitri	⊢ ( ( 𝜑 ∧ ⊤ ) ↔ 𝜑 )
5	4 1	sylbir	⊢ ( 𝜑 → 𝜓 )