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Theorem ssopab2dv 4715
 Description: Inference of ordered pair abstraction subclass from implication. (Contributed by NM, 19-Jan-2014.) (Revised by Mario Carneiro, 24-Jun-2014.)
Hypothesis
Ref Expression
ssopab2dv.1 (φ → (ψχ))
Assertion
Ref Expression
ssopab2dv (φ → {x, y ψ} {x, y χ})
Distinct variable groups:   φ,x   φ,y
Allowed substitution hints:   ψ(x,y)   χ(x,y)

Proof of Theorem ssopab2dv
StepHypRef Expression
1 ssopab2dv.1 . . 3 (φ → (ψχ))
21alrimivv 1632 . 2 (φxy(ψχ))
3 ssopab2 4712 . 2 (xy(ψχ) → {x, y ψ} {x, y χ})
42, 3syl 15 1 (φ → {x, y ψ} {x, y χ})
 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:  xpss12  4855  coss1  4872  coss2  4873  cnvss  4885
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