Description: Proposition 55 of Frege1879 p. 50. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | frege55cor1a | ⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜓 ↔ 𝜑 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege55a | ⊢ ( ( 𝜑 ↔ 𝜓 ) → if- ( 𝜓 , 𝜑 , ¬ 𝜑 ) ) | |
2 | frege55lem1a | ⊢ ( ( ( 𝜑 ↔ 𝜓 ) → if- ( 𝜓 , 𝜑 , ¬ 𝜑 ) ) → ( ( 𝜑 ↔ 𝜓 ) → ( 𝜓 ↔ 𝜑 ) ) ) | |
3 | 1 2 | ax-mp | ⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜓 ↔ 𝜑 ) ) |