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Theorem 3anidm12p2 38502
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
3anidm12p2.1 ((𝜓𝜑𝜑) → 𝜒)
Assertion
Ref Expression
3anidm12p2 ((𝜑𝜓) → 𝜒)

Proof of Theorem 3anidm12p2
StepHypRef Expression
1 3anrot 1041 . . 3 ((𝜓𝜑𝜑) ↔ (𝜑𝜑𝜓))
2 3anidm12p2.1 . . 3 ((𝜓𝜑𝜑) → 𝜒)
31, 2sylbir 225 . 2 ((𝜑𝜑𝜓) → 𝜒)
433anidm12 1380 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
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  df-3an 1038
This theorem is referenced by: (None)
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