Description: The property of being a connected graph. (Contributed by Alexander van der Vekens, 2-Dec-2017) (Revised by AV, 15-Feb-2021)
Ref | Expression | ||
---|---|---|---|
Hypothesis | isconngr.v | |
|
Assertion | isconngr1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isconngr.v | |
|
2 | dfconngr1 | |
|
3 | 2 | eleq2i | |
4 | fvex | |
|
5 | id | |
|
6 | difeq1 | |
|
7 | 6 | raleqdv | |
8 | 5 7 | raleqbidv | |
9 | 4 8 | sbcie | |
10 | 9 | abbii | |
11 | 10 | eleq2i | |
12 | fveq2 | |
|
13 | 12 1 | eqtr4di | |
14 | 13 | difeq1d | |
15 | fveq2 | |
|
16 | 15 | oveqd | |
17 | 16 | breqd | |
18 | 17 | 2exbidv | |
19 | 14 18 | raleqbidv | |
20 | 13 19 | raleqbidv | |
21 | fveq2 | |
|
22 | 21 | difeq1d | |
23 | fveq2 | |
|
24 | 23 | oveqd | |
25 | 24 | breqd | |
26 | 25 | 2exbidv | |
27 | 22 26 | raleqbidv | |
28 | 21 27 | raleqbidv | |
29 | 28 | cbvabv | |
30 | 20 29 | elab2g | |
31 | 11 30 | syl5bb | |
32 | 3 31 | syl5bb | |