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Mirrors > Home > MPE Home > Th. List > elpreima | Structured version Visualization version Unicode version |
Description: Membership in the preimage of a set under a function. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
elpreima |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvimass 5485 | . . . . 5 | |
2 | 1 | sseli 3599 | . . . 4 |
3 | fndm 5990 | . . . . 5 | |
4 | 3 | eleq2d 2687 | . . . 4 |
5 | 2, 4 | syl5ib 234 | . . 3 |
6 | fnfun 5988 | . . . . 5 | |
7 | fvimacnvi 6331 | . . . . 5 | |
8 | 6, 7 | sylan 488 | . . . 4 |
9 | 8 | ex 450 | . . 3 |
10 | 5, 9 | jcad 555 | . 2 |
11 | fvimacnv 6332 | . . . . 5 | |
12 | 11 | funfni 5991 | . . . 4 |
13 | 12 | biimpd 219 | . . 3 |
14 | 13 | expimpd 629 | . 2 |
15 | 10, 14 | impbid 202 | 1 |
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