Description: If a property is true for some ordinal number, it is true for a minimal ordinal number. This version uses implicit substitution. Theorem Schema 62 of Suppes p. 228. (Contributed by NM, 3-Oct-2003)
Ref | Expression | ||
---|---|---|---|
Hypotheses | onminsb.1 | |
|
onminsb.2 | |
||
Assertion | onminsb | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | onminsb.1 | |
|
2 | onminsb.2 | |
|
3 | rabn0 | |
|
4 | ssrab2 | |
|
5 | onint | |
|
6 | 4 5 | mpan | |
7 | 3 6 | sylbir | |
8 | nfrab1 | |
|
9 | 8 | nfint | |
10 | nfcv | |
|
11 | 9 10 1 2 | elrabf | |
12 | 11 | simprbi | |
13 | 7 12 | syl | |