meran3 - Mathbox for Anthony Hart

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Theorem meran3 32412

Description: A single axiom for propositional calculus offered by Meredith. (Contributed by Anthony Hart, 13-Aug-2011.)

**Assertion**
Ref	Expression
meran3	$\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$

**Proof of Theorem meran3**
Step	Hyp	Ref	Expression
1		pm2.3 596	. . . . . 6 $\/$ $\/$ $\/$ $\/$
2	1	imim2i 16	. . . . 5 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
3		pm1.5 544	. . . . 5 $\/$ $\/$ $\/$ $\/$
4	2, 3	syl6 35	. . . 4 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
5		imor 428	. . . 4 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
6		imor 428	. . . 4 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
7	4, 5, 6	3imtr3i 280	. . 3 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
8		meran1 32410	. . . 4 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
9	8	imorri 430	. . 3 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
10	7, 9	syl 17	. 2 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
11	10	imori 429	1 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4 $\/$ wo 383

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

This theorem is referenced by: (None)