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Theorem ssrabi 37621
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 4067 1 {𝑥𝐴𝜑} ⊆ {𝑥𝐴𝜓}
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  {crab 3424  wss 3941
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-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-nfc 2877  df-ral 3054  df-rab 3425  df-v 3468  df-in 3948  df-ss 3958
This theorem is referenced by:  refrelsredund4  38006
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