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Mirrors > Home > MPE Home > Th. List > mulrndx | Structured version Visualization version GIF version |
Description: Index value of the df-mulr 16579 slot. (Contributed by Mario Carneiro, 14-Aug-2015.) |
Ref | Expression |
---|---|
mulrndx | ⊢ (.r‘ndx) = 3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mulr 16579 | . 2 ⊢ .r = Slot 3 | |
2 | 3nn 11717 | . 2 ⊢ 3 ∈ ℕ | |
3 | 1, 2 | ndxarg 16508 | 1 ⊢ (.r‘ndx) = 3 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ‘cfv 6355 3c3 11694 ndxcnx 16480 .rcmulr 16566 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 ax-sep 5203 ax-nul 5210 ax-pow 5266 ax-pr 5330 ax-un 7461 ax-cnex 10593 ax-1cn 10595 ax-addcl 10597 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3or 1084 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-mo 2622 df-eu 2654 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ne 3017 df-ral 3143 df-rex 3144 df-reu 3145 df-rab 3147 df-v 3496 df-sbc 3773 df-csb 3884 df-dif 3939 df-un 3941 df-in 3943 df-ss 3952 df-pss 3954 df-nul 4292 df-if 4468 df-pw 4541 df-sn 4568 df-pr 4570 df-tp 4572 df-op 4574 df-uni 4839 df-iun 4921 df-br 5067 df-opab 5129 df-mpt 5147 df-tr 5173 df-id 5460 df-eprel 5465 df-po 5474 df-so 5475 df-fr 5514 df-we 5516 df-xp 5561 df-rel 5562 df-cnv 5563 df-co 5564 df-dm 5565 df-rn 5566 df-res 5567 df-ima 5568 df-pred 6148 df-ord 6194 df-on 6195 df-lim 6196 df-suc 6197 df-iota 6314 df-fun 6357 df-fn 6358 df-f 6359 df-f1 6360 df-fo 6361 df-f1o 6362 df-fv 6363 df-ov 7159 df-om 7581 df-wrecs 7947 df-recs 8008 df-rdg 8046 df-nn 11639 df-2 11701 df-3 11702 df-ndx 16486 df-slot 16487 df-mulr 16579 |
This theorem is referenced by: plusgndxnmulrndx 16617 basendxnmulrndx 16618 rngstr 16619 opprlem 19378 cnfldfun 20557 matsca 21024 matvsca 21025 |
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