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Mirrors > Home > MPE Home > Th. List > deceq1i | Structured version Visualization version GIF version |
Description: Equality theorem for the decimal constructor. (Contributed by Mario Carneiro, 17-Apr-2015.) |
Ref | Expression |
---|---|
deceq1i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
deceq1i | ⊢ ;𝐴𝐶 = ;𝐵𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | deceq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | deceq1 12736 | . 2 ⊢ (𝐴 = 𝐵 → ;𝐴𝐶 = ;𝐵𝐶) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ;𝐴𝐶 = ;𝐵𝐶 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ;cdc 12731 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1540 df-fal 1550 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-rab 3434 df-v 3480 df-dif 3966 df-un 3968 df-ss 3980 df-nul 4340 df-if 4532 df-sn 4632 df-pr 4634 df-op 4638 df-uni 4913 df-br 5149 df-iota 6516 df-fv 6571 df-ov 7434 df-dec 12732 |
This theorem is referenced by: deceq12i 12740 decmul10add 12800 1mhdrd 32883 hgt750lem2 34646 sqn5ii 42300 fmtno5lem4 47481 fmtno5fac 47507 |
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