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Theorem cbv3h 1983
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
cbv3h.1 (φyφ)
cbv3h.2 (ψxψ)
cbv3h.3 (x = y → (φψ))
Assertion
Ref Expression
cbv3h (xφyψ)

Proof of Theorem cbv3h
StepHypRef Expression
1 cbv3h.1 . . . 4 (φyφ)
21a1i 10 . . 3 (y = y → (φyφ))
3 cbv3h.2 . . . 4 (ψxψ)
43a1i 10 . . 3 (y = y → (ψxψ))
5 cbv3h.3 . . . 4 (x = y → (φψ))
65a1i 10 . . 3 (y = y → (x = y → (φψ)))
72, 4, 6cbv1h 1978 . 2 (xy y = y → (xφyψ))
8 stdpc6 1687 . 2 y y = y
97, 8mpg 1548 1 (xφyψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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:  cleqh  2450
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