 New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  csbeq2dv GIF version

Theorem csbeq2dv 3161
 Description: Formula-building deduction rule for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)
Hypothesis
Ref Expression
csbeq2dv.1 (φB = C)
Assertion
Ref Expression
csbeq2dv (φ[A / x]B = [A / x]C)
Distinct variable group:   φ,x
Allowed substitution hints:   A(x)   B(x)   C(x)

Proof of Theorem csbeq2dv
StepHypRef Expression
1 nfv 1619 . 2 xφ
2 csbeq2dv.1 . 2 (φB = C)
31, 2csbeq2d 3160 1 (φ[A / x]B = [A / x]C)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  [csb 3136 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-sbc 3047  df-csb 3137 This theorem is referenced by:  csbeq2i  3162  fmpt2x  5730
 Copyright terms: Public domain W3C validator