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Theorem 19.42 1575
Description: Theorem 19.42 of [Margaris] p. 90. (Contributed by NM, 18-Aug-1993.)
Hypothesis
Ref Expression
19.42.1 xφ
Assertion
Ref Expression
19.42 (x(φ ψ) ↔ (φ xψ))

Proof of Theorem 19.42
StepHypRef Expression
1 19.42.1 . . 3 xφ
2119.41 1573 . 2 (x(ψ φ) ↔ (xψ φ))
3 exancom 1496 . 2 (x(φ ψ) ↔ x(ψ φ))
4 ancom 253 . 2 ((φ xψ) ↔ (xψ φ))
52, 3, 43bitr4i 201 1 (x(φ ψ) ↔ (φ xψ))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98  wnf 1346  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-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  eean  1803  r2exf  2336
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