Theorem subneg2-P4 538

Description: Alternate Form of subneg-P3.39 323. †

Hypotheses

Ref	Expression
subneg2-P4.1	⊢ (𝛾 → ¬ 𝜑)
subneg2-P4.2	⊢ (𝛾 → (𝜑 ↔ 𝜓))

Assertion

Ref	Expression
subneg2-P4	⊢ (𝛾 → ¬ 𝜓)

Proof of Theorem subneg2-P4

Step	Hyp	Ref	Expression
1		subneg2-P4.1	. 2 ⊢ (𝛾 → ¬ 𝜑)
2		subneg2-P4.2	. . . 4 ⊢ (𝛾 → (𝜑 ↔ 𝜓))
3	2	subneg-P3.39 323	. . 3 ⊢ (𝛾 → (¬ 𝜑 ↔ ¬ 𝜓))
4	3	ndbief-P3.14 179	. 2 ⊢ (𝛾 → (¬ 𝜑 → ¬ 𝜓))
5	1, 4	ndime-P3.6 171	1 ⊢ (𝛾 → ¬ 𝜓)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ↔ wff-bi 104

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-rcp-AND3 161

This theorem is referenced by:  subneg2-P4.RC  539