Theorem merco2 1569

Description: A single axiom for propositional calculus offered by Meredith.

This axiom has 19 symbols, sans auxiliaries. See notes in merco1 1546. (Contributed by Anthony Hart, 7-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
merco2

Proof of Theorem merco2

Step	Hyp	Ref	Expression
1		falim 1409	. . . . . 6
2		pm2.04 82	. . . . . 6
3	1, 2	mpi 17	. . . . 5
4		jarl 163	. . . . . 6
5		idd 24	. . . . . 6
6	4, 5	jad 162	. . . . 5
7		looinv 182	. . . . 5
8	3, 6, 7	3syl 20	. . . 4
9	8	a1dd 46	. . 3
10	9	a1i 11	. 2
11	10	com4l 84	1

Syntax hints:  ->wi 4  wfal 1400

This theorem is referenced by:  mercolem1  1570  mercolem2  1571  mercolem3  1572  mercolem4  1573  mercolem5  1574  mercolem6  1575  mercolem7  1576  mercolem8  1577  re1tbw4  1581

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 185  df-tru 1398  df-fal 1401