Theorem simpri 111

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

Hypothesis

Ref	Expression
simpri.1	⊢ (𝜑 ∧ 𝜓)

Assertion

Ref	Expression
simpri	⊢ 𝜓

Proof of Theorem simpri

Step	Hyp	Ref	Expression
1		simpri.1	. 2 ⊢ (𝜑 ∧ 𝜓)
2		simpr 108	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
3	1, 2	ax-mp 7	1 ⊢ 𝜓

Syntax hints:   ∧ wa 102

This theorem was proved from axioms:  ax-mp 7  ax-ia2 105

This theorem is referenced by:  bi3  117  dfbi2  380  olc  665  mptxor  1356  sb4bor  1758  ordsoexmid  4333  negiso  8152  infrenegsupex  8815