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Theorem ssrabi 34955
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 3937 1 {𝑥𝐴𝜑} ⊆ {𝑥𝐴𝜓}
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2050  {crab 3086  wss 3823
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-ext 2744
This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-clab 2753  df-cleq 2765  df-clel 2840  df-nfc 2912  df-ral 3087  df-rab 3091  df-in 3830  df-ss 3837
This theorem is referenced by:  refrelsredund4  35312
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