Mathbox for Glauco Siliprandi |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > xnegeqi | Structured version Visualization version GIF version |
Description: Equality of two extended numbers with -𝑒 in front of them. (Contributed by Glauco Siliprandi, 2-Jan-2022.) |
Ref | Expression |
---|---|
xnegeqi.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
xnegeqi | ⊢ -𝑒𝐴 = -𝑒𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xnegeqi.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | xnegeq 12683 | . 2 ⊢ (𝐴 = 𝐵 → -𝑒𝐴 = -𝑒𝐵) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ -𝑒𝐴 = -𝑒𝐵 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 -𝑒cxne 12587 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-10 2145 ax-12 2179 ax-ext 2710 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 df-3an 1090 df-tru 1545 df-ex 1787 df-nf 1791 df-sb 2075 df-clab 2717 df-cleq 2730 df-clel 2811 df-rab 3062 df-v 3400 df-un 3848 df-in 3850 df-ss 3860 df-if 4415 df-sn 4517 df-pr 4519 df-op 4523 df-uni 4797 df-br 5031 df-iota 6297 df-fv 6347 df-ov 7173 df-neg 10951 df-xneg 12590 |
This theorem is referenced by: supminfxr2 42549 liminfvalxr 42866 liminf0 42876 liminfpnfuz 42899 |
Copyright terms: Public domain | W3C validator |