New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  mo4 GIF version

Theorem mo4 2237
 Description: "At most one" expressed using implicit substitution. (Contributed by NM, 26-Jul-1995.)
Hypothesis
Ref Expression
mo4.1 (x = y → (φψ))
Assertion
Ref Expression
mo4 (∃*xφxy((φ ψ) → x = y))
Distinct variable groups:   x,y   φ,y   ψ,x
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem mo4
StepHypRef Expression
1 nfv 1619 . 2 xψ
2 mo4.1 . 2 (x = y → (φψ))
31, 2mo4f 2236 1 (∃*xφxy((φ ψ) → x = y))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358  ∀wal 1540  ∃*wmo 2205 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-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209 This theorem is referenced by:  eu4  2243  rmo4  3029  dffun3  5120  dff13  5471  caovmo  5645  xpassen  6057  enpw1  6062
 Copyright terms: Public domain W3C validator