Theorem ss2abi

Description: Inference of abstraction subclass from implication. (Contributed by NM, 31-Mar-1995)

	Ref	Expression
Hypothesis	ss2abi.1	⊢ ( 𝜑 → 𝜓 )
Assertion	ss2abi	⊢ { 𝑥 ∣ 𝜑 } ⊆ { 𝑥 ∣ 𝜓 }

Proof

Step	Hyp	Ref	Expression
1		ss2abi.1	⊢ ( 𝜑 → 𝜓 )
2		ss2ab	⊢ ( { 𝑥 ∣ 𝜑 } ⊆ { 𝑥 ∣ 𝜓 } ↔ ∀ 𝑥 ( 𝜑 → 𝜓 ) )
3	2 1	mpgbir	⊢ { 𝑥 ∣ 𝜑 } ⊆ { 𝑥 ∣ 𝜓 }