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Mathbox for Glauco Siliprandi |
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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 12454 | . 2 ⊢ (𝐴 = 𝐵 → -𝑒𝐴 = -𝑒𝐵) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ -𝑒𝐴 = -𝑒𝐵 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1525 -𝑒cxne 12358 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1781 ax-4 1795 ax-5 1892 ax-6 1951 ax-7 1996 ax-8 2085 ax-9 2093 ax-10 2114 ax-11 2128 ax-12 2143 ax-ext 2771 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 843 df-3an 1082 df-tru 1528 df-ex 1766 df-nf 1770 df-sb 2045 df-clab 2778 df-cleq 2790 df-clel 2865 df-nfc 2937 df-rex 3113 df-rab 3116 df-v 3442 df-dif 3868 df-un 3870 df-in 3872 df-ss 3880 df-nul 4218 df-if 4388 df-sn 4479 df-pr 4481 df-op 4485 df-uni 4752 df-br 4969 df-iota 6196 df-fv 6240 df-ov 7026 df-neg 10726 df-xneg 12361 |
This theorem is referenced by: supminfxr2 41308 liminfvalxr 41627 liminf0 41637 liminfpnfuz 41660 |
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