NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  reximi2 GIF version

Theorem reximi2 2720
Description: Inference quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 8-Nov-2004.)
Hypothesis
Ref Expression
reximi2.1 ((x A φ) → (x B ψ))
Assertion
Ref Expression
reximi2 (x A φx B ψ)

Proof of Theorem reximi2
StepHypRef Expression
1 reximi2.1 . . 3 ((x A φ) → (x B ψ))
21eximi 1576 . 2 (x(x A φ) → x(x B ψ))
3 df-rex 2620 . 2 (x A φx(x A φ))
4 df-rex 2620 . 2 (x B ψx(x B ψ))
52, 3, 43imtr4i 257 1 (x A φx B ψ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358  wex 1541   wcel 1710  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
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-rex 2620
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator