Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  uun121p1 Structured version   Visualization version   GIF version

Theorem uun121p1 41116
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
uun121p1.1 (((𝜑𝜓) ∧ 𝜑) → 𝜒)
Assertion
Ref Expression
uun121p1 ((𝜑𝜓) → 𝜒)

Proof of Theorem uun121p1
StepHypRef Expression
1 anabs1 660 . 2 (((𝜑𝜓) ∧ 𝜑) ↔ (𝜑𝜓))
2 uun121p1.1 . 2 (((𝜑𝜓) ∧ 𝜑) → 𝜒)
31, 2sylbir 237 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398
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 209  df-an 399
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator