Description: Substitution of equal classes into the negation of a binary relation. (Contributed by Glauco Siliprandi, 3-Jan-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | eqnbrtrd.1 | |- ( ph -> A = B ) |
|
eqnbrtrd.2 | |- ( ph -> -. B R C ) |
||
Assertion | eqnbrtrd | |- ( ph -> -. A R C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqnbrtrd.1 | |- ( ph -> A = B ) |
|
2 | eqnbrtrd.2 | |- ( ph -> -. B R C ) |
|
3 | 1 | breq1d | |- ( ph -> ( A R C <-> B R C ) ) |
4 | 2 3 | mtbird | |- ( ph -> -. A R C ) |