Theorem falseprofelimr-P4.7b.RC 396

Description: Inference Form of falseprofelimr-P4.7b 395. †

Hypotheses

Ref	Expression
falseprofelimr-P4.7b.RC.1	⊢ (𝜑 ∨ 𝜓)
falseprofelimr-P4.7b.RC.2	⊢ (𝜓 → ⊥)

Assertion

Ref	Expression
falseprofelimr-P4.7b.RC	⊢ 𝜑

Proof of Theorem falseprofelimr-P4.7b.RC

Step	Hyp	Ref	Expression
1		falseprofelimr-P4.7b.RC.1	. . . 4 ⊢ (𝜑 ∨ 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 ∨ 𝜓))
3		falseprofelimr-P4.7b.RC.2	. . . 4 ⊢ (𝜓 → ⊥)
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜓 → ⊥))
5	2, 4	falseprofelimr-P4.7b 395	. 2 ⊢ (⊤ → 𝜑)
6	5	ndtruee-P3.18 183	1 ⊢ 𝜑

Syntax hints:   → wff-imp 10   ∨ wff-or 144  ⊤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-or-D2.3 145  df-true-D2.4 155  df-false-D2.5 158

This theorem is referenced by: (None)