NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  a16gb GIF version

Theorem a16gb 2050
Description: A generalization of axiom ax-16 2144. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
a16gb (x x = y → (φzφ))
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y,z)

Proof of Theorem a16gb
StepHypRef Expression
1 a16g 1945 . 2 (x x = y → (φzφ))
2 sp 1747 . 2 (zφφ)
31, 2impbid1 194 1 (x x = y → (φzφ))
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  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545
This theorem is referenced by:  sbal  2127
  Copyright terms: Public domain W3C validator