Theorem simpli 444

Description: Inference eliminating a conjunct. (Contributed by NM, 15-Jun-1994.)

Hypothesis

Ref	Expression
simpli.1	⊢ (φ ∧ ψ)

Assertion

Ref	Expression
simpli	⊢ φ

Proof of Theorem simpli

Step	Hyp	Ref	Expression
1		simpli.1	. 2 ⊢ (φ ∧ ψ)
2		simpl 443	. 2 ⊢ ((φ ∧ ψ) → φ)
3	1, 2	ax-mp 5	1 ⊢ φ

This proof depends on syntax axioms:   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)