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Theorem cbvalvw 1702
 Description: Change bound variable. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 9-Apr-2017.)
Hypothesis
Ref Expression
cbvalvw.1 (x = y → (φψ))
Assertion
Ref Expression
cbvalvw (xφyψ)
Distinct variable groups:   x,y   ψ,x   φ,y
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem cbvalvw
StepHypRef Expression
1 cbvalvw.1 . . . 4 (x = y → (φψ))
21biimpd 198 . . 3 (x = y → (φψ))
32cbvalivw 1674 . 2 (xφyψ)
41biimprd 214 . . . 4 (x = y → (ψφ))
54equcoms 1681 . . 3 (y = x → (ψφ))
65cbvalivw 1674 . 2 (yψxφ)
73, 6impbii 180 1 (xφyψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀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 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542 This theorem is referenced by:  cbvexvw  1703  hba1w  1707  ax11wdemo  1723
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