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Theorem rabbidv 2543
Description: Equivalent wff's yield equal restricted class abstractions (deduction rule). (Contributed by NM, 10-Feb-1995.)
Hypothesis
Ref Expression
rabbidv.1 (φ → (ψχ))
Assertion
Ref Expression
rabbidv (φ → {x Aψ} = {x Aχ})
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)   A(x)

Proof of Theorem rabbidv
StepHypRef Expression
1 rabbidv.1 . . 3 (φ → (ψχ))
21adantr 261 . 2 ((φ x A) → (ψχ))
32rabbidva 2542 1 (φ → {x Aψ} = {x Aχ})
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1242   wcel 1390  {crab 2304
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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  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-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-ral 2305  df-rab 2309
This theorem is referenced by:  rabeqbidv  2546  difeq2  3050  seex  4057  mptiniseg  4758  genpdflem  6490  genipv  6492  genpelxp  6494  addcomprg  6554  mulcomprg  6556  uzval  8251  ixxval  8535  fzval  8646
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