NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  19.40 GIF version

Theorem 19.40 1609
Description: Theorem 19.40 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.40 (x(φ ψ) → (xφ xψ))

Proof of Theorem 19.40
StepHypRef Expression
1 exsimpl 1592 . 2 (x(φ ψ) → xφ)
2 simpr 447 . . 3 ((φ ψ) → ψ)
32eximi 1576 . 2 (x(φ ψ) → xψ)
41, 3jca 518 1 (x(φ ψ) → (xφ xψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
This theorem is referenced by:  19.40-2  1610  19.41  1879  exdistrf  1971  uniin  3911  copsexg  4607  dmin  4913  imadif  5171  fv3  5341
  Copyright terms: Public domain W3C validator