Theorem simpr2 948

Description: Simplification rule. (Contributed by Jeff Hankins, 17-Nov-2009.)

Assertion

Ref	Expression
simpr2	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜒)

Proof of Theorem simpr2

Step	Hyp	Ref	Expression
1		simp2 942	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜒)
2	1	adantl 271	1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 102   ∧ w3a 922

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 924

This theorem is referenced by:  simplr2  984  simprr2  990  simp1r2  1038  simp2r2  1044  simp3r2  1050  3anandis  1281  isopolem  5562  tfrlemibacc  6045  tfrlemibfn  6047  tfr1onlembacc  6061  tfr1onlembfn  6063  tfrcllembacc  6074  tfrcllembfn  6076  prltlu  6990  prdisj  6995  prmuloc2  7070  eluzuzle  8959  elioc2  9286  elico2  9287  elicc2  9288  fseq1p1m1  9438  fz0fzelfz0  9466  iseqf1olemp  9836  ibcval5  10068  hashdifpr  10125  isummolem2  10663  isumss2  10673  dvds2ln  10711  divalglemeunn  10803  divalglemex  10804  divalglemeuneg  10805