NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  r19.21 GIF version

Theorem r19.21 2700
Description: Theorem 19.21 of [Margaris] p. 90 with restricted quantifiers. (Contributed by Scott Fenton, 30-Mar-2011.)
Hypothesis
Ref Expression
r19.21.1 xφ
Assertion
Ref Expression
r19.21 (x A (φψ) ↔ (φx A ψ))

Proof of Theorem r19.21
StepHypRef Expression
1 r19.21.1 . 2 xφ
2 r19.21t 2699 . 2 (Ⅎxφ → (x A (φψ) ↔ (φx A ψ)))
31, 2ax-mp 5 1 (x A (φψ) ↔ (φx A ψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wnf 1544  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-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-ral 2619
This theorem is referenced by:  r19.21v  2701
  Copyright terms: Public domain W3C validator