This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Infer double substitution into both sides of a logical equivalence.
(Contributed by AV, 30-Jul-2023)
|
|
Ref |
Expression |
|
Hypothesis |
sbbii.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
|
Assertion |
2sbbii |
⊢ ( [ 𝑡 / 𝑥 ] [ 𝑢 / 𝑦 ] 𝜑 ↔ [ 𝑡 / 𝑥 ] [ 𝑢 / 𝑦 ] 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
sbbii.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
| 2 |
1
|
sbbii |
⊢ ( [ 𝑢 / 𝑦 ] 𝜑 ↔ [ 𝑢 / 𝑦 ] 𝜓 ) |
| 3 |
2
|
sbbii |
⊢ ( [ 𝑡 / 𝑥 ] [ 𝑢 / 𝑦 ] 𝜑 ↔ [ 𝑡 / 𝑥 ] [ 𝑢 / 𝑦 ] 𝜓 ) |