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Mirrors > Home > MPE Home > Th. List > tfrlem3a | Structured version Visualization version Unicode version |
Description: Lemma for transfinite recursion. Let be the class of "acceptable" functions. The final thing we're interested in is the union of all these acceptable functions. This lemma just changes some bound variables in for later use. (Contributed by NM, 9-Apr-1995.) |
Ref | Expression |
---|---|
tfrlem3.1 | |
tfrlem3.2 |
Ref | Expression |
---|---|
tfrlem3a |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfrlem3.2 | . 2 | |
2 | fneq12 5984 | . . . 4 | |
3 | simpll 790 | . . . . . . 7 | |
4 | simpr 477 | . . . . . . 7 | |
5 | 3, 4 | fveq12d 6197 | . . . . . 6 |
6 | 3, 4 | reseq12d 5397 | . . . . . . 7 |
7 | 6 | fveq2d 6195 | . . . . . 6 |
8 | 5, 7 | eqeq12d 2637 | . . . . 5 |
9 | simplr 792 | . . . . 5 | |
10 | 8, 9 | cbvraldva2 3175 | . . . 4 |
11 | 2, 10 | anbi12d 747 | . . 3 |
12 | 11 | cbvrexdva 3178 | . 2 |
13 | tfrlem3.1 | . 2 | |
14 | 1, 12, 13 | elab2 3354 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wceq 1483 wcel 1990 cab 2608 wral 2912 wrex 2913 cvv 3200 cres 5116 con0 5723 wfn 5883 cfv 5888 |
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-res 5126 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 |
This theorem is referenced by: tfrlem3 7474 tfrlem5 7476 tfrlem9a 7482 |
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