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Theorem vtocl2ga 2922
 Description: Implicit substitution of 2 classes for 2 setvar variables. (Contributed by NM, 20-Aug-1995.)
Hypotheses
Ref Expression
vtocl2ga.1 (x = A → (φψ))
vtocl2ga.2 (y = B → (ψχ))
vtocl2ga.3 ((x C y D) → φ)
Assertion
Ref Expression
vtocl2ga ((A C B D) → χ)
Distinct variable groups:   x,y,A   y,B   x,C,y   x,D,y   ψ,x   χ,y
Allowed substitution hints:   φ(x,y)   ψ(y)   χ(x)   B(x)

Proof of Theorem vtocl2ga
StepHypRef Expression
1 nfcv 2489 . 2 xA
2 nfcv 2489 . 2 yA
3 nfcv 2489 . 2 yB
4 nfv 1619 . 2 xψ
5 nfv 1619 . 2 yχ
6 vtocl2ga.1 . 2 (x = A → (φψ))
7 vtocl2ga.2 . 2 (y = B → (ψχ))
8 vtocl2ga.3 . 2 ((x C y D) → φ)
91, 2, 3, 4, 5, 6, 7, 8vtocl2gaf 2921 1 ((A C B D) → χ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358   = wceq 1642   ∈ wcel 1710 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-v 2861 This theorem is referenced by:  f1fveq  5473  caovcan  5628
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