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 4558 | . 2 | |
4 | 1, 2, 3 | syl2anc 408 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 cxp 4537 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-opab 3990 df-xp 4545 |
This theorem is referenced by: sqxpeqd 4565 opeliunxp 4594 mpomptsx 6095 dmmpossx 6097 fmpox 6098 disjxp1 6133 erssxp 6452 fsum2dlemstep 11203 fisumcom2 11207 txbas 12427 |
Copyright terms: Public domain | W3C validator |