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Mirrors > Home > MPE Home > Th. List > Mathboxes > frrlem2 | Structured version Visualization version Unicode version |
Description: Lemma for founded recursion. An acceptable function is a function. (Contributed by Paul Chapman, 21-Apr-2012.) |
Ref | Expression |
---|---|
frrlem1.1 |
Ref | Expression |
---|---|
frrlem2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frrlem1.1 | . . . 4 | |
2 | 1 | frrlem1 31780 | . . 3 |
3 | 2 | abeq2i 2735 | . 2 |
4 | fnfun 5988 | . . . 4 | |
5 | 4 | adantr 481 | . . 3 |
6 | 5 | exlimiv 1858 | . 2 |
7 | 3, 6 | sylbi 207 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wceq 1483 wex 1704 wcel 1990 cab 2608 wral 2912 wss 3574 cres 5116 cpred 5679 wfun 5882 wfn 5883 cfv 5888 (class class class)co 6650 |
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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 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-pred 5680 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 df-ov 6653 |
This theorem is referenced by: frrlem4 31783 frrlem5 31784 frrlem5b 31785 frrlem6 31789 |
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