This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 3-Aug-1994)
|
|
Ref |
Expression |
|
Hypothesis |
biantrur.1 |
⊢ 𝜑 |
|
Assertion |
biantrur |
⊢ ( 𝜓 ↔ ( 𝜑 ∧ 𝜓 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
biantrur.1 |
⊢ 𝜑 |
| 2 |
1
|
biantru |
⊢ ( 𝜓 ↔ ( 𝜓 ∧ 𝜑 ) ) |
| 3 |
2
|
biancomi |
⊢ ( 𝜓 ↔ ( 𝜑 ∧ 𝜓 ) ) |