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Theorem uun111 39801
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
uun111.1 ((𝜑𝜑𝜑) → 𝜓)
Assertion
Ref Expression
uun111 (𝜑𝜓)

Proof of Theorem uun111
StepHypRef Expression
1 3anass 1117 . . 3 ((𝜑𝜑𝜑) ↔ (𝜑 ∧ (𝜑𝜑)))
2 anabs5 654 . . 3 ((𝜑 ∧ (𝜑𝜑)) ↔ (𝜑𝜑))
3 anidm 561 . . 3 ((𝜑𝜑) ↔ 𝜑)
41, 2, 33bitri 289 . 2 ((𝜑𝜑𝜑) ↔ 𝜑)
5 uun111.1 . 2 ((𝜑𝜑𝜑) → 𝜓)
64, 5sylbir 227 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 385  w3a 1108
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 199  df-an 386  df-3an 1110
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator