Description: Conversion of implicit substitution to explicit class substitution, using a bound-variable hypothesis instead of distinct variables. (Closed theorem version of sbciegf .) (Contributed by NM, 10-Nov-2005) (Revised by Mario Carneiro, 13-Oct-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | sbciegft | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbc5 | |
|
2 | biimp | |
|
3 | 2 | imim2i | |
4 | 3 | impd | |
5 | 4 | alimi | |
6 | 19.23t | |
|
7 | 6 | biimpa | |
8 | 5 7 | sylan2 | |
9 | 8 | 3adant1 | |
10 | 1 9 | syl5bi | |
11 | biimpr | |
|
12 | 11 | imim2i | |
13 | 12 | com23 | |
14 | 13 | alimi | |
15 | 19.21t | |
|
16 | 15 | biimpa | |
17 | 14 16 | sylan2 | |
18 | 17 | 3adant1 | |
19 | sbc6g | |
|
20 | 19 | 3ad2ant1 | |
21 | 18 20 | sylibrd | |
22 | 10 21 | impbid | |