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Theorem cbvaliw 1673
 Description: Change bound variable. Uses only Tarski's FOL axiom schemes. Part of Lemma 7 of [KalishMontague] p. 86. (Contributed by NM, 19-Apr-2017.)
Hypotheses
Ref Expression
cbvaliw.1 (xφyxφ)
cbvaliw.2 ψx ¬ ψ)
cbvaliw.3 (x = y → (φψ))
Assertion
Ref Expression
cbvaliw (xφyψ)
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)   ψ(x,y)

Proof of Theorem cbvaliw
StepHypRef Expression
1 cbvaliw.1 . 2 (xφyxφ)
2 cbvaliw.2 . . 3 ψx ¬ ψ)
3 cbvaliw.3 . . 3 (x = y → (φψ))
42, 3spimw 1668 . 2 (xφψ)
51, 4alrimih 1565 1 (xφyψ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀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-9 1654 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542 This theorem is referenced by:  cbvalw  1701
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