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Theorem 3impdirp1 38511
Description: A deduction unionizing a non-unionized collection of virtual hypotheses. Commuted version of 3impdir 1379. (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 466 . . 3 (((𝜒𝜓) ∧ (𝜑𝜓)) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
2 3impdirp1.1 . . 3 (((𝜒𝜓) ∧ (𝜑𝜓)) → 𝜃)
31, 2sylbir 225 . 2 (((𝜑𝜓) ∧ (𝜒𝜓)) → 𝜃)
433impdir 1379 1 ((𝜑𝜒𝜓) → 𝜃)
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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