Theorem truthtbltbif-P4.39b 508

Description: ( T ↔ F ) ⇔ F. †

Assertion

Ref	Expression
truthtbltbif-P4.39b	⊢ ((⊤ ↔ ⊥) ↔ ⊥)

Proof of Theorem truthtbltbif-P4.39b

Step	Hyp	Ref	Expression
1		true-P3.44 352	. . . . 5 ⊢ ⊤
2	1	rcp-NDIMP0addall 207	. . . 4 ⊢ ((⊤ ↔ ⊥) → ⊤)
3		ndbief-P3.14.CL 249	. . . 4 ⊢ ((⊤ ↔ ⊥) → (⊤ → ⊥))
4	2, 3	ndime-P3.6 171	. . 3 ⊢ ((⊤ ↔ ⊥) → ⊥)
5	4	ndfalsee-P3.20 185	. 2 ⊢ ¬ (⊤ ↔ ⊥)
6	5	nthmeqfalse-P4.21b 443	1 ⊢ ((⊤ ↔ ⊥) ↔ ⊥)

Syntax hints:   ↔ wff-bi 104  ⊤wff-true 153  ⊥wff-false 157

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-true-D2.4 155  df-false-D2.5 158

This theorem is referenced by: (None)