tsna1 - Mathbox for Giovanni Mascellani

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Theorem tsna1 33951

Description: A Tseitin axiom for logical incompatibility, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)

**Assertion**
Ref	Expression
tsna1	$\/$ $\/$ $-/\$

**Proof of Theorem tsna1**
Step	Hyp	Ref	Expression
1		tsan1 33948	. 2 $\/$ $\/$ $/\$
2		notnotb 304	. . . . 5 $-/\$ $-/\$
3		df-nan 1448	. . . . 5 $-/\$ $/\$
4	2, 3	bitr3i 266	. . . 4 $-/\$ $/\$
5	4	con4bii 311	. . 3 $-/\$ $/\$
6	5	orbi2i 541	. 2 $\/$ $\/$ $-/\$ $\/$ $\/$ $/\$
7	1, 6	sylibr 224	1 $\/$ $\/$ $-/\$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4 $\/$ wo 383 $/\$ wa 384 $-/\$ wnan 1447

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 df-an 386 df-nan 1448

This theorem is referenced by: (None)