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Metamath Proof Explorer
Description: Theorem *4.86 of WhiteheadRussell p. 122. (Contributed by NM, 3-Jan-2005)
|
|
Ref |
Expression |
|
Assertion |
bibi1 |
⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜑 ↔ 𝜒 ) ↔ ( 𝜓 ↔ 𝜒 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
id |
⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) ) |
| 2 |
1
|
bibi1d |
⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜑 ↔ 𝜒 ) ↔ ( 𝜓 ↔ 𝜒 ) ) ) |