Description: Equivalence of ordered pair abstraction subclass and implication. Compare ssopab2b . Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by FL, 6-Nov-2013) (Proof shortened by Mario Carneiro, 11-Dec-2016) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | ssoprab2b | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfoprab1 | |
|
2 | nfoprab1 | |
|
3 | 1 2 | nfss | |
4 | nfoprab2 | |
|
5 | nfoprab2 | |
|
6 | 4 5 | nfss | |
7 | nfoprab3 | |
|
8 | nfoprab3 | |
|
9 | 7 8 | nfss | |
10 | ssel | |
|
11 | oprabid | |
|
12 | oprabid | |
|
13 | 10 11 12 | 3imtr3g | |
14 | 9 13 | alrimi | |
15 | 6 14 | alrimi | |
16 | 3 15 | alrimi | |
17 | ssoprab2 | |
|
18 | 16 17 | impbii | |