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Theorem ax11v 2096
 Description: This is a version of ax-11o 2141 when the variables are distinct. Axiom (C8) of [Monk2] p. 105. See theorem ax11v2 1992 for the rederivation of ax-11o 2141 from this theorem. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ax11v (x = y → (φx(x = yφ)))
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)

Proof of Theorem ax11v
StepHypRef Expression
1 ax-1 5 . . . 4 (φ → (x = yφ))
2 ax16 2045 . . . 4 (x x = y → ((x = yφ) → x(x = yφ)))
31, 2syl5 28 . . 3 (x x = y → (φx(x = yφ)))
43a1d 22 . 2 (x x = y → (x = y → (φx(x = yφ))))
5 ax11o 1994 . 2 x x = y → (x = y → (φx(x = yφ))))
64, 5pm2.61i 156 1 (x = y → (φx(x = yφ)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  sb56  2098  exsb  2130
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