Theorem falseimpoe-P4.4c.RC 384

Description: Inference Form of falseimpoe-P4.4c 383. †

In an inconsistent system, every wff is a theorem.

Hypothesis

Ref	Expression
falseimpoe-P4.4c.RC.1	⊢ ⊥

Assertion

Ref	Expression
falseimpoe-P4.4c.RC	⊢ 𝜑

Proof of Theorem falseimpoe-P4.4c.RC

Step	Hyp	Ref	Expression
1		falseimpoe-P4.4c.RC.1	. . . 4 ⊢ ⊥
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → ⊥)
3	2	falseimpoe-P4.4c 383	. 2 ⊢ (⊤ → 𝜑)
4	3	ndtruee-P3.18 183	1 ⊢ 𝜑

Syntax hints:  ⊤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

This theorem is referenced by: (None)