Theorem simp-6l 783

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 732	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 206  df-an 396

This theorem is referenced by:  ghmcmn  19348  ustuqtop2  23302  ustuqtop4  23304  cnheibor  24024  miriso  26935  f1otrg  27136  txomap  31686  pstmxmet  31749  omssubadd  32167  signstfvneq0  32451  iunconnlem2  42444  suplesup  42768  limcleqr  43075  0ellimcdiv  43080  limclner  43082  fourierdlem51  43588  smflimlem2  44194