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Mirrors > Home > MPE Home > Th. List > Mathboxes > ax6e2eq | Structured version Visualization version Unicode version |
Description: Alternate form of ax6e 2250 for non-distinct , and . ax6e2eq 38773 is derived from ax6e2eqVD 39143. (Contributed by Alan Sare, 25-Mar-2014.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax6e2eq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax6ev 1890 | . . . . . . 7 | |
2 | hbae 2315 | . . . . . . . 8 | |
3 | ax7 1943 | . . . . . . . . . 10 | |
4 | 3 | sps 2055 | . . . . . . . . 9 |
5 | 4 | ancld 576 | . . . . . . . 8 |
6 | 2, 5 | eximdh 1791 | . . . . . . 7 |
7 | 1, 6 | mpi 20 | . . . . . 6 |
8 | 7 | axc4i 2131 | . . . . 5 |
9 | axc11 2314 | . . . . 5 | |
10 | 8, 9 | mpd 15 | . . . 4 |
11 | 19.2 1892 | . . . 4 | |
12 | 10, 11 | syl 17 | . . 3 |
13 | excomim 2043 | . . 3 | |
14 | 12, 13 | syl 17 | . 2 |
15 | equtrr 1949 | . . . 4 | |
16 | 15 | anim2d 589 | . . 3 |
17 | 16 | 2eximdv 1848 | . 2 |
18 | 14, 17 | syl5com 31 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wal 1481 wex 1704 |
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-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 |
This theorem is referenced by: ax6e2ndeq 38775 ax6e2ndeqVD 39145 ax6e2ndeqALT 39167 |
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