Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > cardval3ex | Unicode version |
Description: The value of . (Contributed by Jim Kingdon, 30-Aug-2021.) |
Ref | Expression |
---|---|
cardval3ex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | encv 6724 | . . . 4 | |
2 | 1 | simprd 113 | . . 3 |
3 | 2 | rexlimivw 2583 | . 2 |
4 | breq1 3992 | . . . 4 | |
5 | 4 | cbvrexv 2697 | . . 3 |
6 | intexrabim 4139 | . . 3 | |
7 | 5, 6 | sylbir 134 | . 2 |
8 | breq2 3993 | . . . . 5 | |
9 | 8 | rabbidv 2719 | . . . 4 |
10 | 9 | inteqd 3836 | . . 3 |
11 | df-card 7157 | . . 3 | |
12 | 10, 11 | fvmptg 5572 | . 2 |
13 | 3, 7, 12 | syl2anc 409 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 wrex 2449 crab 2452 cvv 2730 cint 3831 class class class wbr 3989 con0 4348 cfv 5198 cen 6716 ccrd 7156 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-sbc 2956 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-int 3832 df-br 3990 df-opab 4051 df-mpt 4052 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-iota 5160 df-fun 5200 df-fv 5206 df-en 6719 df-card 7157 |
This theorem is referenced by: oncardval 7163 carden2bex 7166 |
Copyright terms: Public domain | W3C validator |