Theorem falseimpoe-P4.4c 383

Description: Principle of Explosion Utilising '⊥'. †

Hypothesis

Ref	Expression
falseimpoe-P4.4c.1	⊢ (𝛾 → ⊥)

Assertion

Ref	Expression
falseimpoe-P4.4c	⊢ (𝛾 → 𝜑)

Proof of Theorem falseimpoe-P4.4c

Step	Hyp	Ref	Expression
1		falseimpoe-P4.4c.1	. . 3 ⊢ (𝛾 → ⊥)
2	1	ndfalsee-P3.20 185	. 2 ⊢ ¬ 𝛾
3	2	impoe-P4.4a.RC 378	1 ⊢ (𝛾 → 𝜑)

Syntax hints:   → wff-imp 10  ⊥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:  falseimpoe-P4.4c.RC  384  falseprofeliml-P4.7a  393  falseprofelimr-P4.7b  395  falsenegi-P4.18  432  idorfalsel-P4.20a  440  nthmeqfalse-P4.21b  443  truthtblfimt-P4.36c  497