New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  r19.42v GIF version

Theorem r19.42v 2765
 Description: Restricted version of Theorem 19.42 of [Margaris] p. 90. (Contributed by NM, 27-May-1998.)
Assertion
Ref Expression
r19.42v (x A (φ ψ) ↔ (φ x A ψ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem r19.42v
StepHypRef Expression
1 r19.41v 2764 . 2 (x A (ψ φ) ↔ (x A ψ φ))
2 ancom 437 . . 3 ((φ ψ) ↔ (ψ φ))
32rexbii 2639 . 2 (x A (φ ψ) ↔ x A (ψ φ))
4 ancom 437 . 2 ((φ x A ψ) ↔ (x A ψ φ))
51, 3, 43bitr4i 268 1 (x A (φ ψ) ↔ (φ x A ψ))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358  ∃wrex 2615 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-rex 2620 This theorem is referenced by:  ceqsrexbv  2973  ceqsrex2v  2974  2reuswap  3038  2reu5  3044  iunrab  4013  iunin2  4030  iundif2  4033  addcass  4415  elxp2  4802  cnvuni  4895  f1oiso  5499
 Copyright terms: Public domain W3C validator