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Theorem cbval2v 1795
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 4-Feb-2005.)
Hypothesis
Ref Expression
cbval2v.1 ((x = z y = w) → (φψ))
Assertion
Ref Expression
cbval2v (xyφzwψ)
Distinct variable groups:   z,w,φ   x,y,ψ   x,w   y,z
Allowed substitution hints:   φ(x,y)   ψ(z,w)

Proof of Theorem cbval2v
StepHypRef Expression
1 nfv 1418 . 2 zφ
2 nfv 1418 . 2 wφ
3 nfv 1418 . 2 xψ
4 nfv 1418 . 2 yψ
5 cbval2v.1 . 2 ((x = z y = w) → (φψ))
61, 2, 3, 4, 5cbval2 1793 1 (xyφzwψ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  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  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by: (None)
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