bj-peircecurry - Mathbox for BJ

	Mathbox for BJ		< Previous Next > Nearby theorems
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-peircecurry		Structured version Visualization version Unicode version

Theorem bj-peircecurry 32545

Description: Peirce's axiom peirce 193 implies Curry's axiom over minimal implicational calculus and the axiomatic definition of disjunction (olc 399, orc 400, jao 534). See comment of bj-currypeirce 32544. (Contributed by BJ, 15-Jun-2021.) (Proof modification is discouraged.) (New usage is discouraged.)

**Assertion**
Ref	Expression
bj-peircecurry	$\/$

**Proof of Theorem bj-peircecurry**
Step	Hyp	Ref	Expression
1		orc 400	. 2 $\/$
2		olc 399	. . 3 $\/$
3		peirce 193	. . . 4 $\/$ $\/$ $\/$
4		peirce 193	. . . . 5
5		peirceroll 85	. . . . 5 $\/$ $\/$
6	4, 5	ax-mp 5	. . . 4 $\/$ $\/$
7		peirceroll 85	. . . 4 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
8	3, 6, 7	mpsyl 68	. . 3 $\/$ $\/$ $\/$
9	2, 8	ax-mp 5	. 2 $\/$ $\/$
10	1, 9	ax-mp 5	1 $\/$

Colors of variables: wff setvar class

Syntax hints:

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)

W3C validator