Theorem pm3.24 496

Description: Law of contradiction. Theorem *3.24 of [WhiteheadRussell] p. 111.

Assertion

Ref	Expression
pm3.24	⊢ ¬ (φ ∧ ¬ φ)

Proof of Theorem pm3.24

Step	Hyp	Ref	Expression
1		exmid 494	. 2 ⊢ (¬ φ ∨ ¬ ¬ φ)
2		ianor 253	. 2 ⊢ (¬ (φ ∧ ¬ φ) ↔ (¬ φ ∨ ¬ ¬ φ))
3	1, 2	mpbir 165	1 ⊢ ¬ (φ ∧ ¬ φ)

Syntax hints:  ¬ wn 1   ∨ wo 195   ∧ wa 196

This theorem is referenced by:  exists2 1073  pssirr 1570  pssn2lp 1571  dfnul2 1709  dfnul3 1710  zfnul 1746  imadif 2714  fiint 3445  kmlem16 3595  zornlem4 3606  nnunb 4520  indstr 4611

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198

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