The Logic Resource Center

The Logic Resource Center

Public Alpha

The Logic Resource Center

Public Alpha

© 2025 The Logic Resource Center, LLC

Disjunction Introduction

The classical principle of logical addition. If something is true, then so is the claim that either it is the case or some arbitary other condition obtains - this is the idea behind Disjunction Introduction.

Constants: ∨
Systems: LRC_F The Logic Book LRC LRC_P LRC_O

Start a Problem →

Disjunction Introduction

i

i.

ϕ

⋮

i

ii.

∨ψϕ

∨I: i

i

i.

ϕ

⋮

i

ii.

∨ϕψ

∨I: i

Forward

Enter the disjunction you wish to add
Cite a line that is one of its disjuncts
Hit Return

Preview shown for the Typed Forward Strict derivation type in the LRC_P system