Theorem simpri 448

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 447	. 2 ⊢ ((φ ∧ ψ) → ψ)
3	1, 2	ax-mp 5	1 ⊢ ψ

Syntax hints:   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is referenced by:  nmembers1lem2  6270