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Mirrors > Home > MPE Home > Th. List > tposeqi | Structured version Visualization version 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 7877 | . 2 ⊢ (𝐹 = 𝐺 → tpos 𝐹 = tpos 𝐺) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ tpos 𝐹 = tpos 𝐺 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1538 tpos ctpos 7874 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 ax-sep 5167 ax-nul 5174 ax-pr 5295 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-rab 3115 df-v 3443 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-nul 4244 df-if 4426 df-sn 4526 df-pr 4528 df-op 4532 df-br 5031 df-opab 5093 df-mpt 5111 df-xp 5525 df-rel 5526 df-cnv 5527 df-co 5528 df-dm 5529 df-res 5531 df-tpos 7875 |
This theorem is referenced by: tposoprab 7911 mattpos1 21061 |
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