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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 7896 | . 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 1537 tpos ctpos 7893 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 ax-sep 5205 ax-nul 5212 ax-pr 5332 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-rab 3149 df-v 3498 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-if 4470 df-sn 4570 df-pr 4572 df-op 4576 df-br 5069 df-opab 5131 df-mpt 5149 df-xp 5563 df-rel 5564 df-cnv 5565 df-co 5566 df-dm 5567 df-res 5569 df-tpos 7894 |
This theorem is referenced by: tposoprab 7930 mattpos1 21067 |
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