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Mirrors > Home > MPE Home > Th. List > Mathboxes > finxpreclem1 | Structured version Visualization version Unicode version |
Description: Lemma for recursion theorems. (Contributed by ML, 17-Oct-2020.) |
Ref | Expression |
---|---|
finxpreclem1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ov 6653 | . 2 | |
2 | eqidd 2623 | . . 3 | |
3 | eleq1a 2696 | . . . . . 6 | |
4 | 3 | anim2d 589 | . . . . 5 |
5 | iftrue 4092 | . . . . 5 | |
6 | 4, 5 | syl6 35 | . . . 4 |
7 | 6 | imp 445 | . . 3 |
8 | 1onn 7719 | . . . 4 | |
9 | 8 | a1i 11 | . . 3 |
10 | elex 3212 | . . 3 | |
11 | 0ex 4790 | . . . 4 | |
12 | 11 | a1i 11 | . . 3 |
13 | 2, 7, 9, 10, 12 | ovmpt2d 6788 | . 2 |
14 | 1, 13 | syl5reqr 2671 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cvv 3200 c0 3915 cif 4086 cop 4183 cuni 4436 cxp 5112 cfv 5888 (class class class)co 6650 cmpt2 6652 com 7065 c1st 7166 c1o 7553 |
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-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-pss 3590 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-tp 4182 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-tr 4753 df-id 5024 df-eprel 5029 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-ord 5726 df-on 5727 df-lim 5728 df-suc 5729 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-om 7066 df-1o 7560 |
This theorem is referenced by: finxp1o 33229 |
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