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Mirrors > Home > MPE Home > Th. List > deceq12i | 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 |
deceq12i.2 | ⊢ 𝐶 = 𝐷 |
Ref | Expression |
---|---|
deceq12i | ⊢ ;𝐴𝐶 = ;𝐵𝐷 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | deceq1i.1 | . . 3 ⊢ 𝐴 = 𝐵 | |
2 | 1 | deceq1i 12099 | . 2 ⊢ ;𝐴𝐶 = ;𝐵𝐶 |
3 | deceq12i.2 | . . 3 ⊢ 𝐶 = 𝐷 | |
4 | 3 | deceq2i 12100 | . 2 ⊢ ;𝐵𝐶 = ;𝐵𝐷 |
5 | 2, 4 | eqtri 2844 | 1 ⊢ ;𝐴𝐶 = ;𝐵𝐷 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ;cdc 12092 |
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 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-rex 3144 df-rab 3147 df-v 3496 df-dif 3938 df-un 3940 df-in 3942 df-ss 3951 df-nul 4291 df-if 4467 df-sn 4561 df-pr 4563 df-op 4567 df-uni 4832 df-br 5059 df-iota 6308 df-fv 6357 df-ov 7153 df-dec 12093 |
This theorem is referenced by: 11multnc 12160 2exp340mod341 43892 |
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