![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > impbida | Unicode version |
Description: Deduce an equivalence from two implications. (Contributed by NM, 17-Feb-2007.) |
Ref | Expression |
---|---|
impbida.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
impbida.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
impbida |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | impbida.1 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 1 | ex 115 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | impbida.2 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 3 | ex 115 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 2, 4 | impbid 129 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: eqrdav 2176 funfvbrb 5631 f1ocnv2d 6077 1stconst 6224 2ndconst 6225 cnvf1o 6228 ersymb 6551 swoer 6565 erth 6581 enen1 6842 enen2 6843 domen1 6844 domen2 6845 xpmapenlem 6851 fidifsnen 6872 fundmfibi 6940 f1dmvrnfibi 6945 ordiso2 7036 omniwomnimkv 7167 enwomnilem 7169 nninfwlpoimlemginf 7176 exmidapne 7261 infregelbex 9600 fzsplit2 10052 fseq1p1m1 10096 elfz2nn0 10114 btwnzge0 10302 modqsubdir 10395 zesq 10641 hashprg 10790 rereb 10874 abslt 11099 absle 11100 maxleastb 11225 maxltsup 11229 xrltmaxsup 11267 xrmaxltsup 11268 iserex 11349 mptfzshft 11452 fsumrev 11453 fprodrev 11629 dvdsadd2b 11849 nn0ob 11915 dfgcd3 12013 dfgcd2 12017 dvdsmulgcd 12028 lcmgcdeq 12085 isprm5 12144 qden1elz 12207 issubmnd 12848 mhmf1o 12866 grpinvid1 12929 grpinvid2 12930 subsubg 13062 ssnmz 13076 0unit 13303 subrgunit 13365 subsubrg 13371 islss3 13471 islss4 13474 cncnp 13769 xmetxpbl 14047 dedekindicc 14150 coseq0q4123 14294 coseq0negpitopi 14296 relogeftb 14325 relogbcxpbap 14422 pwf1oexmid 14788 isomninnlem 14817 apdiff 14835 iswomninnlem 14836 ismkvnnlem 14839 redcwlpolemeq1 14841 |
Copyright terms: Public domain | W3C validator |