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Theorem 19.29r 1509
Description: Variation of Theorem 19.29 of [Margaris] p. 90. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
19.29r ((xφ xψ) → x(φ ψ))

Proof of Theorem 19.29r
StepHypRef Expression
1 19.29 1508 . 2 ((xψ xφ) → x(ψ φ))
2 ancom 253 . 2 ((xφ xψ) ↔ (xψ xφ))
3 exancom 1496 . 2 (x(φ ψ) ↔ x(ψ φ))
41, 2, 33imtr4i 190 1 ((xφ xψ) → x(φ ψ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wal 1240  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
This theorem is referenced by:  19.29r2  1510  19.29x  1511  exan  1580  ax9o  1585  equvini  1638  eu2  1941  intab  3635  imadiflem  4921  bj-inex  9338
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