Description: Inference of restricted abstraction subclass from implication. (Contributed by Peter Mazsa, 26-Oct-2022)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ssrabi.1 | ⊢ ( 𝜑 → 𝜓 ) | |
Assertion | ssrabi | ⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } ⊆ { 𝑥 ∈ 𝐴 ∣ 𝜓 } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssrabi.1 | ⊢ ( 𝜑 → 𝜓 ) | |
2 | 1 | a1i | ⊢ ( 𝑥 ∈ 𝐴 → ( 𝜑 → 𝜓 ) ) |
3 | 2 | ss2rabi | ⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } ⊆ { 𝑥 ∈ 𝐴 ∣ 𝜓 } |