Theorem uunT1p1 42290

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.)

Hypothesis

Ref	Expression
uunT1p1.1	⊢ ((𝜑 ∧ ⊤) → 𝜓)

Assertion

Ref	Expression
uunT1p1	⊢ (𝜑 → 𝜓)

Proof of Theorem uunT1p1

Step	Hyp	Ref	Expression
1		ancom 460	. . 3 ⊢ ((𝜑 ∧ ⊤) ↔ (⊤ ∧ 𝜑))
2		truan 1550	. . 3 ⊢ ((⊤ ∧ 𝜑) ↔ 𝜑)
3	1, 2	bitri 274	. 2 ⊢ ((𝜑 ∧ ⊤) ↔ 𝜑)
4		uunT1p1.1	. 2 ⊢ ((𝜑 ∧ ⊤) → 𝜓)
5	3, 4	sylbir 234	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395  ⊤wtru 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542

This theorem is referenced by: (None)