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Theorem ssrabi 35671
Description: Inference of restricted abstraction subclass from implication. (Contributed by Peter Mazsa, 26-Oct-2022.)
Hypothesis
Ref Expression
ssrabi.1 (𝜑𝜓)
Assertion
Ref Expression
ssrabi {𝑥𝐴𝜑} ⊆ {𝑥𝐴𝜓}

Proof of Theorem ssrabi
StepHypRef Expression
1 ssrabi.1 . . 3 (𝜑𝜓)
21a1i 11 . 2 (𝑥𝐴 → (𝜑𝜓))
32ss2rabi 4004 1 {𝑥𝐴𝜑} ⊆ {𝑥𝐴𝜓}
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2111  {crab 3110  wss 3881
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ral 3111  df-rab 3115  df-v 3443  df-in 3888  df-ss 3898
This theorem is referenced by:  refrelsredund4  36027
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