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Theorem cbval2v 2006
 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 1619 . 2 zφ
2 nfv 1619 . 2 wφ
3 nfv 1619 . 2 xψ
4 nfv 1619 . 2 yψ
5 cbval2v.1 . 2 ((x = z y = w) → (φψ))
61, 2, 3, 4, 5cbval2 2004 1 (xyφzwψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358  ∀wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  nnsucelr  4428  ssfin  4470  fnfrec  6320
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