Theorem dffalse-P3.49 365

Description: Re-derived Chapter 2 '⊥' definition. †

Assertion

Ref	Expression
dffalse-P3.49	⊢ (⊥ ↔ ¬ ⊤)

Proof of Theorem dffalse-P3.49

Step	Hyp	Ref	Expression
1		dffalse-P3.49-L1 363	. 2 ⊢ (⊥ → ¬ ⊤)
2		dffalse-P3.49-L2 364	. 2 ⊢ (¬ ⊤ → ⊥)
3	1, 2	rcp-NDBII0 239	1 ⊢ (⊥ ↔ ¬ ⊤)

Syntax hints:  ¬ wff-neg 9   ↔ 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  df-rcp-AND3 161

This theorem is referenced by:  truthtblnegt-P4.35a  493