Theorem dffalse-P3.49-L1 363

Description: Lemma for dffalse-P3.49 365. †

Assertion

Ref	Expression
dffalse-P3.49-L1	⊢ (⊥ → ¬ ⊤)

Proof of Theorem dffalse-P3.49-L1

Step	Hyp	Ref	Expression
1		false-P3.45 353	. . 3 ⊢ ¬ ⊥
2	1	ndtruei-P3.17 182	. 2 ⊢ (⊤ → ¬ ⊥)
3	2	trnsp-P3.31a.RC 280	1 ⊢ (⊥ → ¬ ⊤)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10  ⊤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:  dffalse-P3.49  365