Description: If x is not free in A and B , it is not free in A C_ B . (Contributed by NM, 27-Dec-1996)
Ref | Expression | ||
---|---|---|---|
Hypotheses | dfss2f.1 | ⊢ Ⅎ 𝑥 𝐴 | |
dfss2f.2 | ⊢ Ⅎ 𝑥 𝐵 | ||
Assertion | nfss | ⊢ Ⅎ 𝑥 𝐴 ⊆ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2f.1 | ⊢ Ⅎ 𝑥 𝐴 | |
2 | dfss2f.2 | ⊢ Ⅎ 𝑥 𝐵 | |
3 | 1 2 | dfss3f | ⊢ ( 𝐴 ⊆ 𝐵 ↔ ∀ 𝑥 ∈ 𝐴 𝑥 ∈ 𝐵 ) |
4 | nfra1 | ⊢ Ⅎ 𝑥 ∀ 𝑥 ∈ 𝐴 𝑥 ∈ 𝐵 | |
5 | 3 4 | nfxfr | ⊢ Ⅎ 𝑥 𝐴 ⊆ 𝐵 |