ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax-5 GIF version

Axiom ax-5 1254
Description: Axiom of Quantified Implication. Axiom C4 of [Monk2] p. 105. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ax-5 (x(φψ) → (xφxψ))

Detailed syntax breakdown of Axiom ax-5
StepHypRef Expression
1 wph . . . 4 wff φ
2 wps . . . 4 wff ψ
31, 2wi 4 . . 3 wff (φψ)
4 vx . . 3 set x
53, 4wal 1253 . 2 wff x(φψ)
61, 4wal 1253 . . 3 wff xφ
72, 4wal 1253 . . 3 wff xψ
86, 7wi 4 . 2 wff (xφxψ)
95, 8wi 4 1 wff (x(φψ) → (xφxψ))
Colors of variables: wff set class
This axiom is referenced by:  alimi  1263  alim  1265  equidqeOLD  1324  ax4  1326  ax5o  1327  a5i  1340
  Copyright terms: Public domain W3C validator