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Theorem vtocl2ga 2615
 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 2175 . 2 xA
2 nfcv 2175 . 2 yA
3 nfcv 2175 . 2 yB
4 nfv 1418 . 2 xψ
5 nfv 1418 . 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 2614 1 ((A 𝐶 B 𝐷) → χ)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98   = wceq 1242   ∈ wcel 1390 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553 This theorem is referenced by:  caovcan  5607  genipv  6492
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