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Theorem 3impdirp1 39562
 Description: A deduction unionizing a non-unionized collection of virtual hypotheses. Commuted version of 3impdir 1443. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
3impdirp1.1 (((𝜒𝜓) ∧ (𝜑𝜓)) → 𝜃)
Assertion
Ref Expression
3impdirp1 ((𝜑𝜒𝜓) → 𝜃)

Proof of Theorem 3impdirp1
StepHypRef Expression
1 ancom 452 . . 3 (((𝜒𝜓) ∧ (𝜑𝜓)) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
2 3impdirp1.1 . . 3 (((𝜒𝜓) ∧ (𝜑𝜓)) → 𝜃)
31, 2sylbir 225 . 2 (((𝜑𝜓) ∧ (𝜒𝜓)) → 𝜃)
433impdir 1443 1 ((𝜑𝜒𝜓) → 𝜃)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 382   ∧ w3a 1070 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 1072 This theorem is referenced by: (None)
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