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Mirrors > Home > MPE Home > Th. List > syl5eqner | Structured version Visualization version Unicode version |
Description: A chained equality inference for inequality. (Contributed by NM, 6-Jun-2012.) (Proof shortened by Wolf Lammen, 19-Nov-2019.) |
Ref | Expression |
---|---|
syl5eqner.1 | |
syl5eqner.2 |
Ref | Expression |
---|---|
syl5eqner |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl5eqner.1 | . . 3 | |
2 | 1 | a1i 11 | . 2 |
3 | syl5eqner.2 | . 2 | |
4 | 2, 3 | eqnetrrd 2862 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wne 2794 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-cleq 2615 df-ne 2795 |
This theorem is referenced by: xpcoidgend 13714 fclsfnflim 21831 ptcmplem2 21857 vieta1lem1 24065 vieta1lem2 24066 signsvfpn 30662 signsvfnn 30663 finxpreclem2 33227 finxp1o 33229 cdleme3h 35522 cdleme7ga 35535 fourierdlem42 40366 |
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