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Theorem uun123 40700
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
uun123.1 ((𝜑𝜒𝜓) → 𝜃)
Assertion
Ref Expression
uun123 ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem uun123
StepHypRef Expression
1 3ancomb 1092 . 2 ((𝜑𝜒𝜓) ↔ (𝜑𝜓𝜒))
2 uun123.1 . 2 ((𝜑𝜒𝜓) → 𝜃)
31, 2sylbir 236 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1080
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 1082
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator