Description: Alternate proof of fnex , derived using the Axiom of Replacement in the form of funimaexg . This version uses ax-pow and ax-un , whereas fnex does not. (Contributed by NM, 14-Aug-1994) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | fnexALT | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnrel | |
|
2 | relssdmrn | |
|
3 | 1 2 | syl | |
4 | 3 | adantr | |
5 | fndm | |
|
6 | 5 | eleq1d | |
7 | 6 | biimpar | |
8 | fnfun | |
|
9 | funimaexg | |
|
10 | 8 9 | sylan | |
11 | imadmrn | |
|
12 | 5 | imaeq2d | |
13 | 11 12 | eqtr3id | |
14 | 13 | eleq1d | |
15 | 14 | biimpar | |
16 | 10 15 | syldan | |
17 | xpexg | |
|
18 | 7 16 17 | syl2anc | |
19 | ssexg | |
|
20 | 4 18 19 | syl2anc | |