New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  2ralbidv GIF version

Theorem 2ralbidv 2656
 Description: Formula-building rule for restricted universal quantifiers (deduction rule). (Contributed by NM, 28-Jan-2006.) (Revised by Szymon Jaroszewicz, 16-Mar-2007.)
Hypothesis
Ref Expression
2ralbidv.1 (φ → (ψχ))
Assertion
Ref Expression
2ralbidv (φ → (x A y B ψx A y B χ))
Distinct variable groups:   φ,x   φ,y
Allowed substitution hints:   ψ(x,y)   χ(x,y)   A(x,y)   B(x,y)

Proof of Theorem 2ralbidv
StepHypRef Expression
1 2ralbidv.1 . . 3 (φ → (ψχ))
21ralbidv 2634 . 2 (φ → (y B ψy B χ))
32ralbidv 2634 1 (φ → (x A y B ψx A y B χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-ral 2619 This theorem is referenced by:  cbvral3v  2845  isoeq1  5482  isoeq2  5483  isoeq3  5484  trd  5921  extd  5923  symd  5924  trrd  5925  antird  5928  antid  5929  connexrd  5930  connexd  5931  iserd  5942
 Copyright terms: Public domain W3C validator