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Mirrors > Home > NFE Home > Th. List > lefinrflx | Unicode version |
Description: Less than or equal to is reflexive. (Contributed by SF, 2-Feb-2015.) |
Ref | Expression |
---|---|
lefinrflx | fin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | peano1 4402 | . . 3 0c Nn | |
2 | addcid1 4405 | . . . 4 0c | |
3 | 2 | eqcomi 2357 | . . 3 0c |
4 | addceq2 4384 | . . . . 5 0c 0c | |
5 | 4 | eqeq2d 2364 | . . . 4 0c 0c |
6 | 5 | rspcev 2955 | . . 3 0c Nn 0c Nn |
7 | 1, 3, 6 | mp2an 653 | . 2 Nn |
8 | opklefing 4448 | . . 3 fin Nn | |
9 | 8 | anidms 626 | . 2 fin Nn |
10 | 7, 9 | mpbiri 224 | 1 fin |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wceq 1642 wcel 1710 wrex 2615 copk 4057 Nn cnnc 4373 0cc0c 4374 cplc 4375 fin clefin 4432 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 ax-sn 4087 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-symdif 3216 df-ss 3259 df-nul 3551 df-pw 3724 df-sn 3741 df-pr 3742 df-int 3927 df-opk 4058 df-1c 4136 df-pw1 4137 df-ins2k 4187 df-ins3k 4188 df-imak 4189 df-sik 4192 df-ssetk 4193 df-0c 4377 df-addc 4378 df-nnc 4379 df-lefin 4440 |
This theorem is referenced by: lenltfin 4469 |
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