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Theorem pm11.53 1772
 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 1750 . . 3 (y(φψ) ↔ (φyψ))
21albii 1356 . 2 (xy(φψ) ↔ x(φyψ))
3 ax-17 1416 . . . 4 (ψxψ)
43hbal 1363 . . 3 (yψxyψ)
5419.23h 1384 . 2 (x(φyψ) ↔ (xφyψ))
62, 5bitri 173 1 (xy(φψ) ↔ (xφyψ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98  ∀wal 1240  ∃wex 1378 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110 This theorem is referenced by: (None)
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