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

Theorem cbvalivw 1674
Description: Change bound variable. Uses only Tarski's FOL axiom schemes. Part of Lemma 7 of [KalishMontague] p. 86. (Contributed by NM, 9-Apr-2017.)
Hypothesis
Ref Expression
cbvalivw.1 (x = y → (φψ))
Assertion
Ref Expression
cbvalivw (xφyψ)
Distinct variable groups:   x,y   ψ,x   φ,y
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem cbvalivw
StepHypRef Expression
1 cbvalivw.1 . . 3 (x = y → (φψ))
21spimvw 1669 . 2 (xφψ)
32alrimiv 1631 1 (xφyψ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1540
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
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
This theorem is referenced by:  cbvalvw  1702  alcomiw  1704  ax10lem1  1936
  Copyright terms: Public domain W3C validator