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Mirrors > Home > NFE Home > Th. List > pw1ss1c | GIF version |
Description: A unit power class is a subset of 1c. (Contributed by SF, 22-Jan-2015.) |
Ref | Expression |
---|---|
pw1ss1c | ⊢ ℘1A ⊆ 1c |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pw1 4137 | . 2 ⊢ ℘1A = (℘A ∩ 1c) | |
2 | inss2 3476 | . 2 ⊢ (℘A ∩ 1c) ⊆ 1c | |
3 | 1, 2 | eqsstri 3301 | 1 ⊢ ℘1A ⊆ 1c |
Colors of variables: wff setvar class |
Syntax hints: ∩ cin 3208 ⊆ wss 3257 ℘cpw 3722 1cc1c 4134 ℘1cpw1 4135 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 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-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 df-pw1 4137 |
This theorem is referenced by: eqpw1 4162 pw111 4170 eqpw1uni 4330 pw1equn 4331 pw1eqadj 4332 sspw1 4335 sspw12 4336 enpw1pw 6075 ce0lenc1 6239 tlenc1c 6240 |
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