Theorem simp-6l 787

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 737	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  19772  ustuqtop2  24198  ustuqtop4  24200  cnheibor  24922  miriso  28754  f1otrg  28955  txomap  34011  pstmxmet  34074  omssubadd  34477  signstfvneq0  34749  iunconnlem2  45284  suplesup  45692  limcleqr  45996  0ellimcdiv  46001  limclner  46003  fourierdlem51  46509  smflimlem2  47124  upfval  49529