NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  19.38 GIF version

Theorem 19.38 1794
Description: Theorem 19.38 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by Wolf Lammen, 2-Jan-2018.)
Assertion
Ref Expression
19.38 ((xφxψ) → x(φψ))

Proof of Theorem 19.38
StepHypRef Expression
1 alnex 1543 . . 3 (x ¬ φ ↔ ¬ xφ)
2 pm2.21 100 . . . 4 φ → (φψ))
32alimi 1559 . . 3 (x ¬ φx(φψ))
41, 3sylbir 204 . 2 xφx(φψ))
5 ax-1 6 . . 3 (ψ → (φψ))
65alimi 1559 . 2 (xψx(φψ))
74, 6ja 153 1 ((xφxψ) → x(φψ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1540  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-ex 1542
This theorem is referenced by:  19.21t  1795  19.23t  1800
  Copyright terms: Public domain W3C validator