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 735	1 ⊢ (((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 397

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 206  df-an 398

This theorem is referenced by:  ghmcmn  19699  ustuqtop2  23747  ustuqtop4  23749  cnheibor  24471  miriso  27952  f1otrg  28153  txomap  32845  pstmxmet  32908  omssubadd  33330  signstfvneq0  33614  iunconnlem2  43744  suplesup  44097  limcleqr  44408  0ellimcdiv  44413  limclner  44415  fourierdlem51  44921  smflimlem2  45536