Theorem nandir-P4.3b 375

Description: Negated Right '∧' Introduction. †

Hypothesis

Ref	Expression
nandir-P4.3b.1	⊢ (𝛾 → ¬ 𝜑)

Assertion

Ref	Expression
nandir-P4.3b	⊢ (𝛾 → ¬ (𝜑 ∧ 𝜓))

Proof of Theorem nandir-P4.3b

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. . 3 ⊢ ((𝛾 ∧ (𝜑 ∧ 𝜓)) → (𝜑 ∧ 𝜓))
2	1	ndander-P3.9 174	. 2 ⊢ ((𝛾 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
3		nandir-P4.3b.1	. . 3 ⊢ (𝛾 → ¬ 𝜑)
4	3	rcp-NDIMP1add1 208	. 2 ⊢ ((𝛾 ∧ (𝜑 ∧ 𝜓)) → ¬ 𝜑)
5	2, 4	rcp-NDNEGI2 219	1 ⊢ (𝛾 → ¬ (𝜑 ∧ 𝜓))

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ∧ wff-and 132

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

This theorem is referenced by:  nandir-P4.3b.RC  376  dmorgbrev-L4.4  455