![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > tposeqd | GIF version |
Description: Equality theorem for transposition. (Contributed by Mario Carneiro, 7-Jan-2017.) |
Ref | Expression |
---|---|
tposeqd.1 | ⊢ (𝜑 → 𝐹 = 𝐺) |
Ref | Expression |
---|---|
tposeqd | ⊢ (𝜑 → tpos 𝐹 = tpos 𝐺) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tposeqd.1 | . 2 ⊢ (𝜑 → 𝐹 = 𝐺) | |
2 | tposeq 6096 | . 2 ⊢ (𝐹 = 𝐺 → tpos 𝐹 = tpos 𝐺) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → tpos 𝐹 = tpos 𝐺) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1312 tpos ctpos 6093 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-rex 2394 df-v 2657 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-br 3894 df-opab 3948 df-mpt 3949 df-xp 4503 df-rel 4504 df-cnv 4505 df-co 4506 df-dm 4507 df-res 4509 df-tpos 6094 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |