This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Theorem *14.272 in WhiteheadRussell p. 193. (Contributed by Andrew
Salmon, 11-Jul-2011)
|
|
Ref |
Expression |
|
Assertion |
iotasbcq |
⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( [ ( ℩ 𝑥 𝜑 ) / 𝑦 ] 𝜒 ↔ [ ( ℩ 𝑥 𝜓 ) / 𝑦 ] 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
iotabi |
⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( ℩ 𝑥 𝜑 ) = ( ℩ 𝑥 𝜓 ) ) |
| 2 |
1
|
sbceq1d |
⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( [ ( ℩ 𝑥 𝜑 ) / 𝑦 ] 𝜒 ↔ [ ( ℩ 𝑥 𝜓 ) / 𝑦 ] 𝜒 ) ) |