Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > xpeq12d | Unicode version |
Description: Equality deduction for Cartesian product. (Contributed by NM, 8-Dec-2013.) |
Ref | Expression |
---|---|
xpeq1d.1 | |
xpeq12d.2 |
Ref | Expression |
---|---|
xpeq12d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpeq1d.1 | . 2 | |
2 | xpeq12d.2 | . 2 | |
3 | xpeq12 4617 | . 2 | |
4 | 1, 2, 3 | syl2anc 409 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 cxp 4596 |
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-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-opab 4038 df-xp 4604 |
This theorem is referenced by: sqxpeqd 4624 opeliunxp 4653 mpomptsx 6157 dmmpossx 6159 fmpox 6160 disjxp1 6195 erssxp 6515 cc2lem 7198 cc2 7199 fsum2dlemstep 11361 fisumcom2 11365 fprod2dlemstep 11549 fprodcom2fi 11553 txbas 12799 |
Copyright terms: Public domain | W3C validator |