Theorem negbicancel-P4.11.RC 420

Description: Inference Form of negbicancel-P4.11 419.

Hypothesis

Ref	Expression
negbicancel-P4.11.RC.1	⊢ (¬ 𝜑 ↔ ¬ 𝜓)

Assertion

Ref	Expression
negbicancel-P4.11.RC	⊢ (𝜑 ↔ 𝜓)

Proof of Theorem negbicancel-P4.11.RC

Step	Hyp	Ref	Expression
1		negbicancel-P4.11.RC.1	. . . 4 ⊢ (¬ 𝜑 ↔ ¬ 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (¬ 𝜑 ↔ ¬ 𝜓))
3	2	negbicancel-P4.11 419	. 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-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161

This theorem is referenced by:  excomm-P6  740