Metamath Proof Explorer
Description: If A is contained in B , then ( A \ C ) is also contained in
B . Deduction form of ssdifss . (Contributed by David Moews, 1-May-2017)
|
|
Ref |
Expression |
|
Hypothesis |
ssdifd.1 |
⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 ) |
|
Assertion |
ssdifssd |
⊢ ( 𝜑 → ( 𝐴 ∖ 𝐶 ) ⊆ 𝐵 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ssdifd.1 |
⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 ) |
2 |
|
ssdifss |
⊢ ( 𝐴 ⊆ 𝐵 → ( 𝐴 ∖ 𝐶 ) ⊆ 𝐵 ) |
3 |
1 2
|
syl |
⊢ ( 𝜑 → ( 𝐴 ∖ 𝐶 ) ⊆ 𝐵 ) |