Theorem false-P2.15 159

Description: '⊥' is refutable.

Assertion

Ref	Expression
false-P2.15	⊢ ¬ ⊥

Proof of Theorem false-P2.15

Step	Hyp	Ref	Expression
1		true-P2.14 156	. 2 ⊢ ⊤
2		df-false-D2.5 158	. . . 4 ⊢ (⊥ ↔ ¬ ⊤)
3	2	bifwd-P2.5a.SH 112	. . 3 ⊢ (⊥ → ¬ ⊤)
4	3	trnsp-P1.15a.SH 77	. 2 ⊢ (⊤ → ¬ ⊥)
5	1, 4	ax-MP 14	1 ⊢ ¬ ⊥

Syntax hints:  ¬ wff-neg 9  ⊤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-true-D2.4 155  df-false-D2.5 158

This theorem is referenced by:  ndfalsee-P3.20  185