# System S7^{0}

[Hughes and Cresswell, 1996]

## Notes

## Based on

The system S7^{0} is S3^{0} plus the
axiom MMp

The system S7^{0} is therefore:

- Definitions
- Rules
- Uniform substitution (US)
- Strict detachment (MP=>)
- Adjunction (given a, b, return a&b)
(AD)
- substitution of strict equivalents.
(EQS)

- Axioms
- M1: (p&q)=>(q&p)
- M2: (p&q)=>p
- M3: ((p&q)&r)=>(p&(q&r))
- M4: p=>(p&p)
- M5: ((p=>q)&(q=>r))=>(p=>r)
- M8: (p=>q)=>(Mp=>Mq)
- S: MMp

[Hughes and Cresswell, 1996, p354]

## Basis for

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This page was last modified on January 24th, 2007