Description: Substitution in an implication with a variable not free in the consequent affects only the antecedent. (Contributed by NM, 14-Nov-2013) (Revised by Mario Carneiro, 4-Oct-2016)
Ref | Expression | ||
---|---|---|---|
Hypothesis | sblim.1 | |- F/ x ps |
|
Assertion | sblim | |- ( [ y / x ] ( ph -> ps ) <-> ( [ y / x ] ph -> ps ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sblim.1 | |- F/ x ps |
|
2 | sbim | |- ( [ y / x ] ( ph -> ps ) <-> ( [ y / x ] ph -> [ y / x ] ps ) ) |
|
3 | 1 | sbf | |- ( [ y / x ] ps <-> ps ) |
4 | 3 | imbi2i | |- ( ( [ y / x ] ph -> [ y / x ] ps ) <-> ( [ y / x ] ph -> ps ) ) |
5 | 2 4 | bitri | |- ( [ y / x ] ( ph -> ps ) <-> ( [ y / x ] ph -> ps ) ) |