Mathbox for Richard Penner |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > ifpor123g | Structured version Visualization version Unicode version |
Description: Disjunction of conditional logical operators. (Contributed by RP, 18-Apr-2020.) |
Ref | Expression |
---|---|
ifpor123g | if- if- |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-or 385 | . . . 4 if- if- if- if- | |
2 | ifpnot23 37823 | . . . . 5 if- if- | |
3 | 2 | imbi1i 339 | . . . 4 if- if- if- if- |
4 | 1, 3 | bitri 264 | . . 3 if- if- if- if- |
5 | ifpim123g 37845 | . . 3 if- if- | |
6 | 4, 5 | bitri 264 | . 2 if- if- |
7 | pm4.64 387 | . . . . 5 | |
8 | 7 | orbi2i 541 | . . . 4 |
9 | pm4.64 387 | . . . . 5 | |
10 | 9 | orbi2i 541 | . . . 4 |
11 | 8, 10 | anbi12i 733 | . . 3 |
12 | pm4.64 387 | . . . . 5 | |
13 | 12 | orbi2i 541 | . . . 4 |
14 | pm4.64 387 | . . . . 5 | |
15 | 14 | orbi2i 541 | . . . 4 |
16 | 13, 15 | anbi12i 733 | . . 3 |
17 | 11, 16 | anbi12i 733 | . 2 |
18 | 6, 17 | bitri 264 | 1 if- if- |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wo 383 wa 384 if-wif 1012 |
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 197 df-or 385 df-an 386 df-ifp 1013 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |