Theorem simpr2 946

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 940	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜒)
2	1	adantl 271	1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 102   ∧ w3a 920

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 922

This theorem is referenced by:  simplr2  982  simprr2  988  simp1r2  1036  simp2r2  1042  simp3r2  1048  3anandis  1279  isopolem  5540  tfrlemibacc  6023  tfrlemibfn  6025  tfr1onlembacc  6039  tfr1onlembfn  6041  tfrcllembacc  6052  tfrcllembfn  6054  prltlu  6949  prdisj  6954  prmuloc2  7029  eluzuzle  8922  elioc2  9249  elico2  9250  elicc2  9251  fseq1p1m1  9401  fz0fzelfz0  9429  ibcval5  10006  hashdifpr  10063  dvds2ln  10609  divalglemeunn  10701  divalglemex  10702  divalglemeuneg  10703