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Mirrors > Home > MPE Home > Th. List > abrexco | Structured version Visualization version Unicode version |
Description: Composition of two image maps and . (Contributed by NM, 27-May-2013.) |
Ref | Expression |
---|---|
abrexco.1 | |
abrexco.2 |
Ref | Expression |
---|---|
abrexco |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2918 | . . . . 5 | |
2 | vex 3203 | . . . . . . . . 9 | |
3 | eqeq1 2626 | . . . . . . . . . 10 | |
4 | 3 | rexbidv 3052 | . . . . . . . . 9 |
5 | 2, 4 | elab 3350 | . . . . . . . 8 |
6 | 5 | anbi1i 731 | . . . . . . 7 |
7 | r19.41v 3089 | . . . . . . 7 | |
8 | 6, 7 | bitr4i 267 | . . . . . 6 |
9 | 8 | exbii 1774 | . . . . 5 |
10 | 1, 9 | bitri 264 | . . . 4 |
11 | rexcom4 3225 | . . . 4 | |
12 | 10, 11 | bitr4i 267 | . . 3 |
13 | abrexco.1 | . . . . 5 | |
14 | abrexco.2 | . . . . . 6 | |
15 | 14 | eqeq2d 2632 | . . . . 5 |
16 | 13, 15 | ceqsexv 3242 | . . . 4 |
17 | 16 | rexbii 3041 | . . 3 |
18 | 12, 17 | bitri 264 | . 2 |
19 | 18 | abbii 2739 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wex 1704 wcel 1990 cab 2608 wrex 2913 cvv 3200 |
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-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-v 3202 |
This theorem is referenced by: rankcf 9599 sylow1lem2 18014 sylow3lem1 18042 restco 20968 |
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