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Theorem chvarv 1790
 Description: Implicit substitution of y for x into a theorem. (Contributed by NM, 20-Apr-1994.)
Hypotheses
Ref Expression
chv.1 (x = y → (φψ))
chv.2 φ
Assertion
Ref Expression
chvarv ψ
Distinct variable group:   ψ,x
Allowed substitution hints:   φ(x,y)   ψ(y)

Proof of Theorem chvarv
StepHypRef Expression
1 chv.1 . . 3 (x = y → (φψ))
21spv 1718 . 2 (xφψ)
3 chv.2 . 2 φ
42, 3mpg 1316 1 ψ
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98 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-gen 1314  ax-ie1 1359  ax-ie2 1360  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:  axext3  2001  axsep2  3846  tz6.12f  5123  tfrlem3-2  5845  bdsep2  7304  strcoll2  7397
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