Theorem ss2abiOLD 4060

Description: Obsolete version of ss2abi 4059 as of 28-Jun-2024. (Contributed by NM, 31-Mar-1995.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
ss2abiOLD.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
ss2abiOLD	⊢ {𝑥 ∣ 𝜑} ⊆ {𝑥 ∣ 𝜓}

Proof of Theorem ss2abiOLD

Step	Hyp	Ref	Expression
1		ss2ab 4053	. 2 ⊢ ({𝑥 ∣ 𝜑} ⊆ {𝑥 ∣ 𝜓} ↔ ∀𝑥(𝜑 → 𝜓))
2		ss2abiOLD.1	. 2 ⊢ (𝜑 → 𝜓)
3	1, 2	mpgbir 1793	1 ⊢ {𝑥 ∣ 𝜑} ⊆ {𝑥 ∣ 𝜓}

Syntax hints:   → wi 4  {cab 2702   ⊆ wss 3944

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-10 2129  ax-11 2146  ax-12 2166

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2703  df-clel 2802  df-nfc 2877  df-ss 3961

This theorem is referenced by: (None)