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Mirrors > Home > MPE Home > Th. List > xp2cda | Structured version Visualization version Unicode version |
Description: Two times a cardinal number. Exercise 4.56(g) of [Mendelson] p. 258. (Contributed by NM, 27-Sep-2004.) (Revised by Mario Carneiro, 29-Apr-2015.) |
Ref | Expression |
---|---|
xp2cda |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdaval 8992 | . . 3 | |
2 | 1 | anidms 677 | . 2 |
3 | df2o3 7573 | . . . . 5 | |
4 | df-pr 4180 | . . . . 5 | |
5 | 3, 4 | eqtri 2644 | . . . 4 |
6 | 5 | xpeq2i 5136 | . . 3 |
7 | xpundi 5171 | . . 3 | |
8 | 6, 7 | eqtri 2644 | . 2 |
9 | 2, 8 | syl6reqr 2675 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 cun 3572 c0 3915 csn 4177 cpr 4179 cxp 5112 (class class class)co 6650 c1o 7553 c2o 7554 ccda 8989 |
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 |
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-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-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-suc 5729 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-1o 7560 df-2o 7561 df-cda 8990 |
This theorem is referenced by: pwcda1 9016 unctb 9027 infcdaabs 9028 ackbij1lem5 9046 fin56 9215 |
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