Description: Corollary of commutation of nor. (Contributed by RP, 25-Apr-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | ifpnorcor | ⊢ ( if- ( 𝜑 , ¬ 𝜑 , ¬ 𝜓 ) ↔ if- ( 𝜓 , ¬ 𝜓 , ¬ 𝜑 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ifporcor | ⊢ ( if- ( 𝜑 , 𝜑 , 𝜓 ) ↔ if- ( 𝜓 , 𝜓 , 𝜑 ) ) | |
2 | 1 | notbii | ⊢ ( ¬ if- ( 𝜑 , 𝜑 , 𝜓 ) ↔ ¬ if- ( 𝜓 , 𝜓 , 𝜑 ) ) |
3 | ifpnot23 | ⊢ ( ¬ if- ( 𝜑 , 𝜑 , 𝜓 ) ↔ if- ( 𝜑 , ¬ 𝜑 , ¬ 𝜓 ) ) | |
4 | ifpnot23 | ⊢ ( ¬ if- ( 𝜓 , 𝜓 , 𝜑 ) ↔ if- ( 𝜓 , ¬ 𝜓 , ¬ 𝜑 ) ) | |
5 | 2 3 4 | 3bitr3i | ⊢ ( if- ( 𝜑 , ¬ 𝜑 , ¬ 𝜓 ) ↔ if- ( 𝜓 , ¬ 𝜓 , ¬ 𝜑 ) ) |