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Theorem uun132 40996
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
uun132.1 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
uun132 ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem uun132
StepHypRef Expression
1 3anass 1087 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
2 uun132.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylbi 218 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1079
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
This theorem is referenced by: (None)
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