Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  uunT11p2 Structured version   Visualization version   GIF version

Theorem uunT11p2 39544
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
uunT11p2.1 ((𝜑𝜑 ∧ ⊤) → 𝜓)
Assertion
Ref Expression
uunT11p2 (𝜑𝜓)

Proof of Theorem uunT11p2
StepHypRef Expression
1 3anrev 1089 . . . 4 ((𝜑𝜑 ∧ ⊤) ↔ (⊤ ∧ 𝜑𝜑))
2 3anass 1079 . . . 4 ((⊤ ∧ 𝜑𝜑) ↔ (⊤ ∧ (𝜑𝜑)))
3 truan 1648 . . . 4 ((⊤ ∧ (𝜑𝜑)) ↔ (𝜑𝜑))
41, 2, 33bitri 286 . . 3 ((𝜑𝜑 ∧ ⊤) ↔ (𝜑𝜑))
5 anidm 546 . . 3 ((𝜑𝜑) ↔ 𝜑)
64, 5bitri 264 . 2 ((𝜑𝜑 ∧ ⊤) ↔ 𝜑)
7 uunT11p2.1 . 2 ((𝜑𝜑 ∧ ⊤) → 𝜓)
86, 7sylbir 225 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1070  wtru 1631
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 197  df-an 383  df-3an 1072  df-tru 1633
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator