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Theorem cbvexvw 1703
 Description: Change bound variable. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 19-Apr-2017.)
Hypothesis
Ref Expression
cbvalvw.1 (x = y → (φψ))
Assertion
Ref Expression
cbvexvw (xφyψ)
Distinct variable groups:   x,y   ψ,x   φ,y
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem cbvexvw
StepHypRef Expression
1 cbvalvw.1 . . . . 5 (x = y → (φψ))
21notbid 285 . . . 4 (x = y → (¬ φ ↔ ¬ ψ))
32cbvalvw 1702 . . 3 (x ¬ φy ¬ ψ)
43notbii 287 . 2 x ¬ φ ↔ ¬ y ¬ ψ)
5 df-ex 1542 . 2 (xφ ↔ ¬ x ¬ φ)
6 df-ex 1542 . 2 (yψ ↔ ¬ y ¬ ψ)
74, 5, 63bitr4i 268 1 (xφyψ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176  ∀wal 1540  ∃wex 1541 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: (None)
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