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Theorem pm11.53 1893
 Description: Theorem *11.53 in [WhiteheadRussell] p. 164. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm11.53 (xy(φψ) ↔ (xφyψ))
Distinct variable groups:   φ,y   ψ,x
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem pm11.53
StepHypRef Expression
1 19.21v 1890 . . 3 (y(φψ) ↔ (φyψ))
21albii 1566 . 2 (xy(φψ) ↔ x(φyψ))
3 nfv 1619 . . . 4 xψ
43nfal 1842 . . 3 xyψ
5419.23 1801 . 2 (x(φyψ) ↔ (xφyψ))
62, 5bitri 240 1 (xy(φψ) ↔ (xφyψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540  ∃wex 1541 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 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by: (None)
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