Theorem nandil-P4.3a 373

Description: Negated Left '∧' Introduction. †

Hypothesis

Ref	Expression
nandil-P4.3a.1	⊢ (𝛾 → ¬ 𝜑)

Assertion

Ref	Expression
nandil-P4.3a	⊢ (𝛾 → ¬ (𝜓 ∧ 𝜑))

Proof of Theorem nandil-P4.3a

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. . 3 ⊢ ((𝛾 ∧ (𝜓 ∧ 𝜑)) → (𝜓 ∧ 𝜑))
2	1	ndandel-P3.8 173	. 2 ⊢ ((𝛾 ∧ (𝜓 ∧ 𝜑)) → 𝜑)
3		nandil-P4.3a.1	. . 3 ⊢ (𝛾 → ¬ 𝜑)
4	3	rcp-NDIMP1add1 208	. 2 ⊢ ((𝛾 ∧ (𝜓 ∧ 𝜑)) → ¬ 𝜑)
5	2, 4	rcp-NDNEGI2 219	1 ⊢ (𝛾 → ¬ (𝜓 ∧ 𝜑))

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:  nandil-P4.3a.RC  374  dmorgbrev-L4.4  455