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Theorem 19.23vv 1892
 Description: Theorem 19.23 of [Margaris] p. 90 extended to two variables. (Contributed by NM, 10-Aug-2004.)
Assertion
Ref Expression
19.23vv (xy(φψ) ↔ (xyφψ))
Distinct variable groups:   ψ,x   ψ,y
Allowed substitution hints:   φ(x,y)

Proof of Theorem 19.23vv
StepHypRef Expression
1 19.23v 1891 . . 3 (y(φψ) ↔ (yφψ))
21albii 1566 . 2 (xy(φψ) ↔ x(yφψ))
3 19.23v 1891 . 2 (x(yφψ) ↔ (xyφψ))
42, 3bitri 240 1 (xy(φψ) ↔ (xyφψ))
 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-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  ssrelk  4211  eqrelk  4212  sikexlem  4295  insklem  4304  raliunxp  4823  ssopr  4846
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