MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  3orcombOLD Structured version   Visualization version   GIF version

Theorem 3orcombOLD 1080
Description: Obsolete version of 3orcomb 1079 as of 8-Apr-2022. (Contributed by Scott Fenton, 20-Apr-2011.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
3orcombOLD ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))

Proof of Theorem 3orcombOLD
StepHypRef Expression
1 orcom 401 . . 3 ((𝜓𝜒) ↔ (𝜒𝜓))
21orbi2i 542 . 2 ((𝜑 ∨ (𝜓𝜒)) ↔ (𝜑 ∨ (𝜒𝜓)))
3 3orass 1075 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
4 3orass 1075 . 2 ((𝜑𝜒𝜓) ↔ (𝜑 ∨ (𝜒𝜓)))
52, 3, 43bitr4i 292 1 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wo 382  w3o 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-or 384  df-3or 1073
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator