NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  ax7w GIF version

Theorem ax7w 1718
Description: Weak version of ax-7 1734 from which we can prove any ax-7 1734 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. Unlike ax-7 1734, this theorem requires that x and y be distinct i.e. are not bundled. (Contributed by NM, 10-Apr-2017.)
Ref Expression
ax7w.1 (y = z → (φψ))
Ref Expression
ax7w (xyφyxφ)
Distinct variable groups:   y,z   x,y   φ,z   ψ,y
Allowed substitution hints:   φ(x,y)   ψ(x,z)

Proof of Theorem ax7w
StepHypRef Expression
1 ax7w.1 . 2 (y = z → (φψ))
21alcomiw 1704 1 (xyφyxφ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator