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Theorem 19.41vv 1902
 Description: Theorem 19.41 of [Margaris] p. 90 with 2 quantifiers. (Contributed by NM, 30-Apr-1995.)
Assertion
Ref Expression
19.41vv (xy(φ ψ) ↔ (xyφ ψ))
Distinct variable groups:   ψ,x   ψ,y
Allowed substitution hints:   φ(x,y)

Proof of Theorem 19.41vv
StepHypRef Expression
1 19.41v 1901 . . 3 (y(φ ψ) ↔ (yφ ψ))
21exbii 1582 . 2 (xy(φ ψ) ↔ x(yφ ψ))
3 19.41v 1901 . 2 (x(yφ ψ) ↔ (xyφ ψ))
42, 3bitri 240 1 (xy(φ ψ) ↔ (xyφ ψ))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358  ∃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-an 360  df-ex 1542  df-nf 1545 This theorem is referenced by:  19.41vvv  1903  pm11.07  2115  dfpw12  4301  ltfinex  4464  setconslem4  4734  setconslem6  4736  rabxp  4814  elres  4995  fnov  5591  mpt2mptx  5708  restxp  5786  lecex  6115
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