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Theorem cbvalv 1791
Description: Rule used to change bound variables, using implicit substitition. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
cbvalv.1 (x = y → (φψ))
Assertion
Ref Expression
cbvalv (xφyψ)
Distinct variable groups:   φ,y   ψ,x
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem cbvalv
StepHypRef Expression
1 ax-17 1416 . 2 (φyφ)
2 ax-17 1416 . 2 (ψxψ)
3 cbvalv.1 . 2 (x = y → (φψ))
41, 2, 3cbvalh 1633 1 (xφyψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1240
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-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  nfcjust  2163  cdeqal1  2749  zfpow  3919  tfisi  4253  acexmid  5454  tfrlem3-2d  5869  tfrlemi1  5887  tfrexlem  5889  genprndl  6503  genprndu  6504
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