Description: Obsolete version of xorcom as of 21-Apr-2024. (Contributed by Mario Carneiro, 4-Sep-2016) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | xorcomOLD | ⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ( 𝜓 ⊻ 𝜑 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bicom | ⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ( 𝜓 ↔ 𝜑 ) ) | |
2 | 1 | notbii | ⊢ ( ¬ ( 𝜑 ↔ 𝜓 ) ↔ ¬ ( 𝜓 ↔ 𝜑 ) ) |
3 | df-xor | ⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ¬ ( 𝜑 ↔ 𝜓 ) ) | |
4 | df-xor | ⊢ ( ( 𝜓 ⊻ 𝜑 ) ↔ ¬ ( 𝜓 ↔ 𝜑 ) ) | |
5 | 2 3 4 | 3bitr4i | ⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ( 𝜓 ⊻ 𝜑 ) ) |