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Theorem 19.38 1539
Description: Theorem 19.38 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.38 ((xφxψ) → x(φψ))

Proof of Theorem 19.38
StepHypRef Expression
1 hbe1 1357 . . 3 (xφxxφ)
2 hba1 1406 . . 3 (xψxxψ)
31, 2hbim 1410 . 2 ((xφxψ) → x(xφxψ))
4 19.8a 1455 . . 3 (φxφ)
5 ax-4 1373 . . 3 (xψψ)
64, 5imim12i 53 . 2 ((xφxψ) → (φψ))
73, 6alrimih 1331 1 ((xφxψ) → x(φψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1221  wex 1354
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 1309  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-4 1373  ax-ial 1400  ax-i5r 1401
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  19.23t  1540  sbi2v  1745  mo3h  1926  rgenm  3291  ralm  3293
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