Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > ceqsalt | Structured version Visualization version Unicode version |
Description: Closed theorem version of ceqsalg 3230. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
ceqsalt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 3215 | . . . 4 | |
2 | 1 | 3ad2ant3 1084 | . . 3 |
3 | biimp 205 | . . . . . . 7 | |
4 | 3 | imim3i 64 | . . . . . 6 |
5 | 4 | al2imi 1743 | . . . . 5 |
6 | 5 | 3ad2ant2 1083 | . . . 4 |
7 | 19.23t 2079 | . . . . 5 | |
8 | 7 | 3ad2ant1 1082 | . . . 4 |
9 | 6, 8 | sylibd 229 | . . 3 |
10 | 2, 9 | mpid 44 | . 2 |
11 | biimpr 210 | . . . . . . 7 | |
12 | 11 | imim2i 16 | . . . . . 6 |
13 | 12 | com23 86 | . . . . 5 |
14 | 13 | alimi 1739 | . . . 4 |
15 | 14 | 3ad2ant2 1083 | . . 3 |
16 | 19.21t 2073 | . . . 4 | |
17 | 16 | 3ad2ant1 1082 | . . 3 |
18 | 15, 17 | mpbid 222 | . 2 |
19 | 10, 18 | impbid 202 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 w3a 1037 wal 1481 wceq 1483 wex 1704 wnf 1708 wcel 1990 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-12 2047 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 |
This theorem is referenced by: ceqsralt 3229 ceqsalg 3230 |
Copyright terms: Public domain | W3C validator |