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Theorem uun121 38489
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
uun121.1 ((𝜑 ∧ (𝜑𝜓)) → 𝜒)
Assertion
Ref Expression
uun121 ((𝜑𝜓) → 𝜒)

Proof of Theorem uun121
StepHypRef Expression
1 anabs5 850 . 2 ((𝜑 ∧ (𝜑𝜓)) ↔ (𝜑𝜓))
2 uun121.1 . 2 ((𝜑 ∧ (𝜑𝜓)) → 𝜒)
31, 2sylbir 225 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 386
This theorem is referenced by: (None)
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