Theorem negbicancelint-P4.14.RC 425

Description: Inference Form of negbicancelint-P4.14 424. †

Hypothesis

Ref	Expression
negbicancelint-P4.14.RC.1	⊢ (¬ ¬ 𝜑 ↔ ¬ ¬ 𝜓)

Assertion

Ref	Expression
negbicancelint-P4.14.RC	⊢ (¬ 𝜑 ↔ ¬ 𝜓)

Proof of Theorem negbicancelint-P4.14.RC

Step	Hyp	Ref	Expression
1		negbicancelint-P4.14.RC.1	. . . 4 ⊢ (¬ ¬ 𝜑 ↔ ¬ ¬ 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (¬ ¬ 𝜑 ↔ ¬ ¬ 𝜓))
3	2	negbicancelint-P4.14 424	. 2 ⊢ (⊤ → (¬ 𝜑 ↔ ¬ 𝜓))
4	3	ndtruee-P3.18 183	1 ⊢ (¬ 𝜑 ↔ ¬ 𝜓)

Syntax hints:  ¬ wff-neg 9   ↔ wff-bi 104  ⊤wff-true 153

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-rcp-AND3 161

This theorem is referenced by: (None)