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Theorem 19.41vv 1780
 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 1779 . . 3 (y(φ ψ) ↔ (yφ ψ))
21exbii 1493 . 2 (xy(φ ψ) ↔ x(yφ ψ))
3 19.41v 1779 . 2 (x(yφ ψ) ↔ (xyφ ψ))
42, 3bitri 173 1 (xy(φ ψ) ↔ (xyφ ψ))
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   ↔ wb 98  ∃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-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  19.41vvv  1781  rabxp  4323  rexiunxp  4421  mpt2mptx  5537  xpassen  6240  dmaddpqlem  6361  nqpi  6362  nqnq0pi  6421  nq0nn  6425
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