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Theorem 3anidm12p1 39558
Description: A deduction unionizing a non-unionized collection of virtual hypotheses. 3anidm12 1529 denotes the deduction which would have been named uun112 if it did not pre-exist in This second permutation's name is based on this pre-existing name. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Ref Expression
3anidm12p1.1 ((𝜑𝜓𝜑) → 𝜒)
Ref Expression
3anidm12p1 ((𝜑𝜓) → 𝜒)

Proof of Theorem 3anidm12p1
StepHypRef Expression
1 3anidm12p1.1 . 2 ((𝜑𝜓𝜑) → 𝜒)
213anidm13 1530 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1071
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 383  df-3an 1073
This theorem is referenced by: (None)
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