Mathbox for Andrew Salmon |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > iotavalb | Structured version Visualization version Unicode version |
Description: Theorem *14.202 in [WhiteheadRussell] p. 189. A biconditional version of iotaval 5862. (Contributed by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
iotavalb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iotaval 5862 | . 2 | |
2 | iotasbc 38620 | . . . 4 | |
3 | iotaexeu 38619 | . . . . 5 | |
4 | eqsbc3 3475 | . . . . 5 | |
5 | 3, 4 | syl 17 | . . . 4 |
6 | 2, 5 | bitr3d 270 | . . 3 |
7 | equequ2 1953 | . . . . . . 7 | |
8 | 7 | bibi2d 332 | . . . . . 6 |
9 | 8 | albidv 1849 | . . . . 5 |
10 | 9 | biimpac 503 | . . . 4 |
11 | 10 | exlimiv 1858 | . . 3 |
12 | 6, 11 | syl6bir 244 | . 2 |
13 | 1, 12 | impbid2 216 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wceq 1483 wex 1704 wcel 1990 weu 2470 cvv 3200 wsbc 3435 cio 5849 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-v 3202 df-sbc 3436 df-un 3579 df-sn 4178 df-pr 4180 df-uni 4437 df-iota 5851 |
This theorem is referenced by: iotavalsb 38634 |
Copyright terms: Public domain | W3C validator |