New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  ssopab2i GIF version

Theorem ssopab2i 4714
 Description: Inference of ordered pair abstraction subclass from implication. (Contributed by NM, 5-Apr-1995.)
Hypothesis
Ref Expression
ssopab2i.1 (φψ)
Assertion
Ref Expression
ssopab2i {x, y φ} {x, y ψ}

Proof of Theorem ssopab2i
StepHypRef Expression
1 ssopab2 4712 . 2 (xy(φψ) → {x, y φ} {x, y ψ})
2 ssopab2i.1 . . 3 (φψ)
32ax-gen 1546 . 2 y(φψ)
41, 3mpg 1548 1 {x, y φ} {x, y ψ}
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540   ⊆ wss 3257  {copab 4622 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  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-opab 4623 This theorem is referenced by:  opabssxp  4837  funopab4  5141  ssoprab2i  5580
 Copyright terms: Public domain W3C validator