Theorem simpli 109

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 107	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
3	1, 2	ax-mp 7	1 ⊢ 𝜑

Syntax hints:   ∧ wa 102

This theorem was proved from axioms:  ax-mp 7  ax-ia1 104

This theorem is referenced by:  bi1  116  bi2  128  dfbi2  380  orc  665  pwundifss  4040  ssdomg  6281  negiso  8033  infrenegsupex  8682