Mathbox for Jarvin Udandy < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  nabctnabc Structured version   Unicode version

Theorem nabctnabc 38238
 Description: not ( a -> ( b /\ c ) ) we can show: not a implies ( b /\ c ) (Contributed by Jarvin Udandy, 7-Sep-2020.)
Hypothesis
Ref Expression
nabctnabc.1
Assertion
Ref Expression
nabctnabc

Proof of Theorem nabctnabc
StepHypRef Expression
1 nabctnabc.1 . . . . . . . 8
2 pm4.61 428 . . . . . . . . 9
32biimpi 198 . . . . . . . 8
41, 3ax-mp 5 . . . . . . 7
54simpli 460 . . . . . 6
64simpri 464 . . . . . 6
75, 62th 243 . . . . 5
8 bicom 204 . . . . . 6
98biimpi 198 . . . . 5
107, 9ax-mp 5 . . . 4
1110biimpi 198 . . 3
1211con3i 141 . 2
1312notnotrd 117 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wa 371 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 189  df-an 373 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator