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Theorem cbvral 2523
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 31-Jul-2003.)
Hypotheses
Ref Expression
cbvral.1 yφ
cbvral.2 xψ
cbvral.3 (x = y → (φψ))
Assertion
Ref Expression
cbvral (x A φy A ψ)
Distinct variable groups:   x,A   y,A
Allowed substitution hints:   φ(x,y)   ψ(x,y)

Proof of Theorem cbvral
StepHypRef Expression
1 nfcv 2175 . 2 xA
2 nfcv 2175 . 2 yA
3 cbvral.1 . 2 yφ
4 cbvral.2 . 2 xψ
5 cbvral.3 . 2 (x = y → (φψ))
61, 2, 3, 4, 5cbvralf 2521 1 (x A φy A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wnf 1346  wral 2300
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-bnd 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-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305
This theorem is referenced by:  cbvralv  2527  cbvralsv  2538  cbviin  3686  ralxpf  4425  eqfnfv2f  5212  ralrnmpt  5252  dff13f  5352  ofrfval2  5669  fmpt2x  5768  indstr  8292  bj-bdfindes  9383  bj-findes  9411
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