This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypothesis |
bnj564.17 |
⊢ ( 𝜏 ↔ ( 𝑓 Fn 𝑚 ∧ 𝜑′ ∧ 𝜓′ ) ) |
|
Assertion |
bnj564 |
⊢ ( 𝜏 → dom 𝑓 = 𝑚 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
bnj564.17 |
⊢ ( 𝜏 ↔ ( 𝑓 Fn 𝑚 ∧ 𝜑′ ∧ 𝜓′ ) ) |
| 2 |
1
|
simp1bi |
⊢ ( 𝜏 → 𝑓 Fn 𝑚 ) |
| 3 |
2
|
fndmd |
⊢ ( 𝜏 → dom 𝑓 = 𝑚 ) |