NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  r19.26-2 GIF version

Theorem r19.26-2 2747
Description: Theorem 19.26 of [Margaris] p. 90 with 2 restricted quantifiers. (Contributed by NM, 10-Aug-2004.)
Assertion
Ref Expression
r19.26-2 (x A y B (φ ψ) ↔ (x A y B φ x A y B ψ))

Proof of Theorem r19.26-2
StepHypRef Expression
1 r19.26 2746 . . 3 (y B (φ ψ) ↔ (y B φ y B ψ))
21ralbii 2638 . 2 (x A y B (φ ψ) ↔ x A (y B φ y B ψ))
3 r19.26 2746 . 2 (x A (y B φ y B ψ) ↔ (x A y B φ x A y B ψ))
42, 3bitri 240 1 (x A y B (φ ψ) ↔ (x A y B φ x A y B ψ))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wa 358  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-tru 1319  df-ex 1542  df-nf 1545  df-ral 2619
This theorem is referenced by:  fununi  5160
  Copyright terms: Public domain W3C validator