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Theorem uun2131p1 41418
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
uun2131p1.1 (((𝜑𝜒) ∧ (𝜑𝜓)) → 𝜃)
Assertion
Ref Expression
uun2131p1 ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem uun2131p1
StepHypRef Expression
1 ancom 464 . . 3 (((𝜑𝜓) ∧ (𝜑𝜒)) ↔ ((𝜑𝜒) ∧ (𝜑𝜓)))
2 uun2131p1.1 . . 3 (((𝜑𝜒) ∧ (𝜑𝜓)) → 𝜃)
31, 2sylbi 220 . 2 (((𝜑𝜓) ∧ (𝜑𝜒)) → 𝜃)
433impdi 1347 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  w3a 1084
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 210  df-an 400  df-3an 1086
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator