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

Theorem sbrim 2067
Description: Substitution with a variable not free in antecedent affects only the consequent. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 4-Oct-2016.)
Hypothesis
Ref Expression
sbrim.1  F/
Assertion
Ref Expression
sbrim

Proof of Theorem sbrim
StepHypRef Expression
1 sbim 2065 . 2
2 sbrim.1 . . . 4  F/
32sbf 2026 . . 3
43imbi1i 315 . 2
51, 4bitri 240 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   F/wnf 1544  wsb 1648
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  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649
This theorem is referenced by:  sbco2d  2087  2mos  2283
  Copyright terms: Public domain W3C validator