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Mirrors > Home > MPE Home > Th. List > lo1mptrcl | Structured version Visualization version Unicode version |
Description: Reverse closure for an eventually upper bounded function. (Contributed by Mario Carneiro, 26-May-2016.) |
Ref | Expression |
---|---|
o1add2.1 | |
lo1mptrcl.3 |
Ref | Expression |
---|---|
lo1mptrcl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lo1mptrcl.3 | . . . . 5 | |
2 | lo1f 14249 | . . . . 5 | |
3 | 1, 2 | syl 17 | . . . 4 |
4 | o1add2.1 | . . . . . . 7 | |
5 | 4 | ralrimiva 2966 | . . . . . 6 |
6 | dmmptg 5632 | . . . . . 6 | |
7 | 5, 6 | syl 17 | . . . . 5 |
8 | 7 | feq2d 6031 | . . . 4 |
9 | 3, 8 | mpbid 222 | . . 3 |
10 | eqid 2622 | . . . 4 | |
11 | 10 | fmpt 6381 | . . 3 |
12 | 9, 11 | sylibr 224 | . 2 |
13 | 12 | r19.21bi 2932 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wral 2912 cmpt 4729 cdm 5114 wf 5884 cr 9935 clo1 14218 |
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-pow 4843 ax-pr 4906 ax-un 6949 ax-cnex 9992 ax-resscn 9993 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 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-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-pm 7860 df-lo1 14222 |
This theorem is referenced by: lo1add 14357 lo1mul 14358 lo1mul2 14359 lo1sub 14361 lo1le 14382 |
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