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Theorem ss2abi 3006
Description: Inference of abstraction subclass from implication. (Contributed by NM, 31-Mar-1995.)
Hypothesis
Ref Expression
ss2abi.1 (φψ)
Assertion
Ref Expression
ss2abi {xφ} ⊆ {xψ}

Proof of Theorem ss2abi
StepHypRef Expression
1 ss2ab 3002 . 2 ({xφ} ⊆ {xψ} ↔ x(φψ))
2 ss2abi.1 . 2 (φψ)
31, 2mpgbir 1339 1 {xφ} ⊆ {xψ}
Colors of variables: wff set class
Syntax hints:  wi 4  {cab 2023  wss 2911
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-in 2918  df-ss 2925
This theorem is referenced by:  abssi  3009  rabssab  3021  pwsnss  3565  iinuniss  3728  abssexg  3925  imassrn  4622  imadiflem  4921  imainlem  4923  fabexg  5020  f1oabexg  5081
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