Description: Theorem *13.18 in WhiteheadRussell p. 178. (Contributed by Andrew Salmon, 3-Jun-2011) (Proof shortened by Wolf Lammen, 14-May-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | pm13.18 | |- ( ( A = B /\ A =/= C ) -> B =/= C ) |
Step | Hyp | Ref | Expression |
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1 | neeq1 | |- ( A = B -> ( A =/= C <-> B =/= C ) ) |
|
2 | 1 | biimpd | |- ( A = B -> ( A =/= C -> B =/= C ) ) |
3 | 2 | imp | |- ( ( A = B /\ A =/= C ) -> B =/= C ) |