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Theorem cbvalv 1772
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 1396 . 2 (φyφ)
2 ax-17 1396 . 2 (ψxψ)
3 cbvalv.1 . 2 (x = y → (φψ))
41, 2, 3cbvalh 1614 1 (xφyψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1224
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 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405
This theorem depends on definitions:  df-bi 110  df-nf 1326
This theorem is referenced by:  nfcjust  2144  cdeqal1  2728  zfpow  3898  tfisi  4233  acexmid  5431  tfrlem3-2d  5846  tfrlemi1  5863  tfrexlem  5866  genprndl  6370  genprndu  6371
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