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Theorem rspc2v 2961
 Description: 2-variable restricted specialization, using implicit substitution. (Contributed by NM, 13-Sep-1999.)
Hypotheses
Ref Expression
rspc2v.1 (x = A → (φχ))
rspc2v.2 (y = B → (χψ))
Assertion
Ref Expression
rspc2v ((A C B D) → (x C y D φψ))
Distinct variable groups:   x,y,A   y,B   x,C   x,D,y   χ,x   ψ,y
Allowed substitution hints:   φ(x,y)   ψ(x)   χ(y)   B(x)   C(y)

Proof of Theorem rspc2v
StepHypRef Expression
1 nfv 1619 . 2 xχ
2 nfv 1619 . 2 yψ
3 rspc2v.1 . 2 (x = A → (φχ))
4 rspc2v.2 . 2 (y = B → (χψ))
51, 2, 3, 4rspc2 2960 1 ((A C B D) → (x C y D φψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358   = wceq 1642   ∈ wcel 1710  ∀wral 2614 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-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861 This theorem is referenced by:  rspc2va  2962  rspc3v  2964  ncfinraise  4481  nnpweq  4523  isorel  5489  isotr  5495  fovcl  5588  caovcld  5622  caovcomg  5624  extd  5923  symd  5924  antid  5929  connexd  5931
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