Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  cbvalw Structured version   Unicode version

Theorem cbvalw 1859
 Description: Change bound variable. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 9-Apr-2017.)
Hypotheses
Ref Expression
cbvalw.1
cbvalw.2
cbvalw.3
cbvalw.4
cbvalw.5
Assertion
Ref Expression
cbvalw
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvalw
StepHypRef Expression
1 cbvalw.1 . . 3
2 cbvalw.2 . . 3
3 cbvalw.5 . . . 4
43biimpd 211 . . 3
51, 2, 4cbvaliw 1838 . 2
6 cbvalw.3 . . 3
7 cbvalw.4 . . 3
83biimprd 227 . . . 4
98equcoms 1846 . . 3
106, 7, 9cbvaliw 1838 . 2
115, 10impbii 191 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188  wal 1436 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840 This theorem depends on definitions:  df-bi 189  df-ex 1661 This theorem is referenced by:  cbvalvw  1860  hbn1fw  1863
 Copyright terms: Public domain W3C validator