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Mirrors > Home > ILE Home > Th. List > tposeqi | GIF version |
Description: Equality theorem for transposition. (Contributed by Mario Carneiro, 10-Sep-2015.) |
Ref | Expression |
---|---|
tposeqi.1 | ⊢ 𝐹 = 𝐺 |
Ref | Expression |
---|---|
tposeqi | ⊢ tpos 𝐹 = tpos 𝐺 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tposeqi.1 | . 2 ⊢ 𝐹 = 𝐺 | |
2 | tposeq 6262 | . 2 ⊢ (𝐹 = 𝐺 → tpos 𝐹 = tpos 𝐺) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ tpos 𝐹 = tpos 𝐺 |
Colors of variables: wff set class |
Syntax hints: = wceq 1363 tpos ctpos 6259 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-br 4016 df-opab 4077 df-mpt 4078 df-xp 4644 df-rel 4645 df-cnv 4646 df-co 4647 df-dm 4648 df-res 4650 df-tpos 6260 |
This theorem is referenced by: tposoprab 6295 |
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