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Mirrors > Home > NFE Home > Th. List > p6eq | Unicode version |
Description: Equality theorem for P6 operation. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
p6eq | P6 P6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq2 3293 | . . 3 k k | |
2 | 1 | abbidv 2467 | . 2 k k |
3 | df-p6 4191 | . 2 P6 k | |
4 | df-p6 4191 | . 2 P6 k | |
5 | 2, 3, 4 | 3eqtr4g 2410 | 1 P6 P6 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 cab 2339 cvv 2859 wss 3257 csn 3737 k cxpk 4174 P6 cp6 4178 |
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 |
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-p6 4191 |
This theorem is referenced by: p6eqi 4239 p6eqd 4240 p6exg 4290 |
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