Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  uunT12p5 Structured version   Visualization version   GIF version

Theorem uunT12p5 41015
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
uunT12p5.1 ((𝜓𝜑 ∧ ⊤) → 𝜒)
Assertion
Ref Expression
uunT12p5 ((𝜑𝜓) → 𝜒)

Proof of Theorem uunT12p5
StepHypRef Expression
1 3anrev 1093 . . . 4 ((𝜓𝜑 ∧ ⊤) ↔ (⊤ ∧ 𝜑𝜓))
2 3anass 1087 . . . 4 ((⊤ ∧ 𝜑𝜓) ↔ (⊤ ∧ (𝜑𝜓)))
31, 2bitri 276 . . 3 ((𝜓𝜑 ∧ ⊤) ↔ (⊤ ∧ (𝜑𝜓)))
4 truan 1539 . . 3 ((⊤ ∧ (𝜑𝜓)) ↔ (𝜑𝜓))
53, 4bitri 276 . 2 ((𝜓𝜑 ∧ ⊤) ↔ (𝜑𝜓))
6 uunT12p5.1 . 2 ((𝜓𝜑 ∧ ⊤) → 𝜒)
75, 6sylbir 236 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1079  wtru 1529
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 208  df-an 397  df-3an 1081  df-tru 1531
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator