Description: Cancellation of a nonzero factor on the right in an equation. One-way deduction form of mulcan2d . (Contributed by David Moews, 28-Feb-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | mulcanad.1 | |- ( ph -> A e. CC ) |
|
mulcanad.2 | |- ( ph -> B e. CC ) |
||
mulcanad.3 | |- ( ph -> C e. CC ) |
||
mulcanad.4 | |- ( ph -> C =/= 0 ) |
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mulcan2ad.5 | |- ( ph -> ( A x. C ) = ( B x. C ) ) |
||
Assertion | mulcan2ad | |- ( ph -> A = B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mulcanad.1 | |- ( ph -> A e. CC ) |
|
2 | mulcanad.2 | |- ( ph -> B e. CC ) |
|
3 | mulcanad.3 | |- ( ph -> C e. CC ) |
|
4 | mulcanad.4 | |- ( ph -> C =/= 0 ) |
|
5 | mulcan2ad.5 | |- ( ph -> ( A x. C ) = ( B x. C ) ) |
|
6 | 1 2 3 4 | mulcan2d | |- ( ph -> ( ( A x. C ) = ( B x. C ) <-> A = B ) ) |
7 | 5 6 | mpbid | |- ( ph -> A = B ) |