Users' Mathboxes Mathbox for Alexander van der Vekens < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  nfich2 Structured version   Visualization version   GIF version

Theorem nfich2 44573
Description: The second interchangeable setvar variable is not free. (Contributed by AV, 21-Aug-2023.)
Assertion
Ref Expression
nfich2 𝑦[𝑥𝑦]𝜑

Proof of Theorem nfich2
Dummy variable 𝑎 is distinct from all other variables.
StepHypRef Expression
1 df-ich 44571 . 2 ([𝑥𝑦]𝜑 ↔ ∀𝑥𝑦([𝑥 / 𝑎][𝑦 / 𝑥][𝑎 / 𝑦]𝜑𝜑))
2 nfa2 2174 . 2 𝑦𝑥𝑦([𝑥 / 𝑎][𝑦 / 𝑥][𝑎 / 𝑦]𝜑𝜑)
31, 2nfxfr 1860 1 𝑦[𝑥𝑦]𝜑
Colors of variables: wff setvar class
Syntax hints:  wb 209  wal 1541  wnf 1791  [wsb 2070  [wich 44570
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-10 2141  ax-11 2158
This theorem depends on definitions:  df-bi 210  df-or 848  df-ex 1788  df-nf 1792  df-ich 44571
This theorem is referenced by:  ich2exprop  44596  ichreuopeq  44598
  Copyright terms: Public domain W3C validator