Theorem ss2abiOLD 3997

Description: Obsolete version of ss2abi 3996 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 3989	. 2 ⊢ ({𝑥 ∣ 𝜑} ⊆ {𝑥 ∣ 𝜓} ↔ ∀𝑥(𝜑 → 𝜓))
2		ss2abiOLD.1	. 2 ⊢ (𝜑 → 𝜓)
3	1, 2	mpgbir 1803	1 ⊢ {𝑥 ∣ 𝜑} ⊆ {𝑥 ∣ 𝜓}

Syntax hints:   → wi 4  {cab 2715   ⊆ wss 3883

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-10 2139  ax-11 2156  ax-12 2173  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-ex 1784  df-nf 1788  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-nfc 2888  df-v 3424  df-in 3890  df-ss 3900

This theorem is referenced by: (None)