Theorem simp-5l 543

Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)

Assertion

Ref	Expression
simp-5l	⊢ ((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜑)

Proof of Theorem simp-5l

Step	Hyp	Ref	Expression
1		simp-4l 541	. 2 ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)
2	1	adantr 276	1 ⊢ ((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  simp-6l  545  aptap  8669  xaddf  9910  nn0ltexp2  10780  xrmaxiflemlub  11391  dfgcd2  12151  ctiunctlemfo  12596  mhmmnd  13186  neitx  14436  limccnp2cntop  14831  limccoap  14832  lgsval  15120