Theorem merco1 1546

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

This axiom is worthy of note, due to it having only 19 symbols, not counting parentheses. The more well-known meredith 1472 has 21 symbols, sans parentheses.

See merco2 1569 for another axiom of equal length. (Contributed by Anthony Hart, 13-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
merco1

Proof of Theorem merco1

Step	Hyp	Ref	Expression
1		ax-1 6	. . . . . 6
2		falim 1409	. . . . . 6
3	1, 2	ja 161	. . . . 5
4	3	imim2i 14	. . . 4
5	4	imim1i 58	. . 3
6	5	imim1i 58	. 2
7		meredith 1472	. 2
8	6, 7	syl 16	1

Syntax hints:  -.wn 3  ->wi 4  wfal 1400

This theorem is referenced by:  merco1lem1  1547  retbwax2  1549  merco1lem2  1550  merco1lem4  1552  merco1lem5  1553  merco1lem6  1554  merco1lem7  1555  merco1lem10  1559  merco1lem11  1560  merco1lem12  1561  merco1lem13  1562  merco1lem14  1563  merco1lem16  1565  merco1lem17  1566  merco1lem18  1567  retbwax1  1568

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