Theorem simp-6l 786

Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.) (Proof shortened by Wolf Lammen, 24-May-2022.)

Assertion

Ref	Expression
simp-6l	⊢ (((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) → 𝜑)

Proof of Theorem simp-6l

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝜑 → 𝜑)
2	1	ad6antr 736	1 ⊢ (((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395

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 207  df-an 396

This theorem is referenced by:  ghmcmn  19741  ustuqtop2  24155  ustuqtop4  24157  cnheibor  24879  miriso  28646  f1otrg  28847  txomap  33842  pstmxmet  33905  omssubadd  34308  signstfvneq0  34580  iunconnlem2  44966  suplesup  45377  limcleqr  45681  0ellimcdiv  45686  limclner  45688  fourierdlem51  46194  smflimlem2  46809  upfval  49207