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Theorem ss2abiOLD 3957
Description: Obsolete version of ss2abi 3956 as of 28-Jun-2024. (Contributed by NM, 31-Mar-1995.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ss2abiOLD.1 (𝜑𝜓)
Assertion
Ref Expression
ss2abiOLD {𝑥𝜑} ⊆ {𝑥𝜓}

Proof of Theorem ss2abiOLD
StepHypRef Expression
1 ss2ab 3949 . 2 ({𝑥𝜑} ⊆ {𝑥𝜓} ↔ ∀𝑥(𝜑𝜓))
2 ss2abiOLD.1 . 2 (𝜑𝜓)
31, 2mpgbir 1806 1 {𝑥𝜑} ⊆ {𝑥𝜓}
Colors of variables: wff setvar class
Syntax hints:  wi 4  {cab 2716  wss 3843
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2162  ax-12 2179  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-tru 1545  df-ex 1787  df-nf 1791  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-nfc 2881  df-v 3400  df-in 3850  df-ss 3860
This theorem is referenced by: (None)
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