Theorem simpli 111

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 109	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
3	1, 2	ax-mp 5	1 ⊢ 𝜑

Syntax hints:   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-ia1 106

This theorem is referenced by:  biimp  118  biimpr  130  dfbi2  388  orc  712  pwundifss  4285  ssdomg  6777  negiso  8911  infrenegsupex  9593  xrnegiso  11269  infxrnegsupex  11270  cos01bnd  11765  cos1bnd  11766  cos2bnd  11767  sin4lt0  11773  egt2lt3  11786  epos  11787  ene1  11791  eap1  11792  slotslfn  12487  strslfvd  12503  strslfv2d  12504  strsl0  12510  setsslid  12512  setsslnid  12513  reeff1o  14130  pigt2lt4  14141  pire  14143  pipos  14145  sinhalfpi  14153  tan4thpi  14198  sincos3rdpi  14200  pigt3  14201  lgsdir2lem4  14368  lgsdir2lem5  14369