MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  sb6x Unicode version

Theorem sb6x 2125
Description: Equivalence involving substitution for a variable not free. (Contributed by NM, 2-Jun-1993.) (Revised by Mario Carneiro, 4-Oct-2016.)
Hypothesis
Ref Expression
sb6x.1
Assertion
Ref Expression
sb6x

Proof of Theorem sb6x
StepHypRef Expression
1 sb6x.1 . . 3
21sbf 2121 . 2
3 biidd 237 . . 3
41, 3equsal 2036 . 2
52, 4bitr4i 252 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  F/wnf 1616  [wsb 1739
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
  Copyright terms: Public domain W3C validator