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Theorem 19.42vvvv 1787
Description: Theorem 19.42 of [Margaris] p. 90 with 4 quantifiers. (Contributed by Jim Kingdon, 23-Nov-2019.)
Assertion
Ref Expression
19.42vvvv (wxyz(φ ψ) ↔ (φ wxyzψ))
Distinct variable groups:   φ,w   φ,x   φ,y   φ,z
Allowed substitution hints:   ψ(x,y,z,w)

Proof of Theorem 19.42vvvv
StepHypRef Expression
1 19.42vv 1785 . . 3 (yz(φ ψ) ↔ (φ yzψ))
212exbii 1494 . 2 (wxyz(φ ψ) ↔ wx(φ yzψ))
3 19.42vv 1785 . 2 (wx(φ yzψ) ↔ (φ wxyzψ))
42, 3bitri 173 1 (wxyz(φ ψ) ↔ (φ wxyzψ))
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:  ceqsex8v  2593  enq0tr  6416
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