Theorem ss2abiOLD 3968

Description: Obsolete version of ss2abi 3967 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 3960	. 2 ⊢ ({𝑥 ∣ 𝜑} ⊆ {𝑥 ∣ 𝜓} ↔ ∀𝑥(𝜑 → 𝜓))
2		ss2abiOLD.1	. 2 ⊢ (𝜑 → 𝜓)
3	1, 2	mpgbir 1802	1 ⊢ {𝑥 ∣ 𝜑} ⊆ {𝑥 ∣ 𝜓}

Syntax hints:   → wi 4  {cab 2736   ⊆ wss 3854

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2730

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 846  df-tru 1542  df-ex 1783  df-nf 1787  df-sb 2071  df-clab 2737  df-cleq 2751  df-clel 2831  df-nfc 2899  df-v 3409  df-in 3861  df-ss 3871

This theorem is referenced by: (None)