Theorem com15 101

Description: Commutation of antecedents. Swap 1st and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.) (Proof shortened by Wolf Lammen, 29-Jul-2012.)

Hypothesis

Ref	Expression
com5.1	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Assertion

Ref	Expression
com15	⊢ (𝜏 → (𝜓 → (𝜒 → (𝜃 → (𝜑 → 𝜂)))))

Proof of Theorem com15

Step	Hyp	Ref	Expression
1		com5.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))
2	1	com5l 100	. 2 ⊢ (𝜓 → (𝜒 → (𝜃 → (𝜏 → (𝜑 → 𝜂)))))
3	2	com4r 94	1 ⊢ (𝜏 → (𝜓 → (𝜒 → (𝜃 → (𝜑 → 𝜂)))))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  injresinjlem  12911  addmodlteq  13068  fi1uzind  13597  brfi1indALT  13600  swrdswrdlem  13817  2cshwcshw  13980  lcmfdvdsb  15766  initoeu1  17050  initoeu2lem1  17053  initoeu2  17055  termoeu1  17057  upgrwlkdvdelem  27092  spthonepeq  27108  usgr2pthlem  27119  erclwwlktr  27415  erclwwlkntr  27473  3cyclfrgrrn1  27697  frgrnbnb  27705  frgrncvvdeqlem8  27718  frgrreg  27830  frgrregord013  27831  zerdivemp1x  34375  bgoldbtbndlem4  42731  bgoldbtbnd  42732  tgoldbach  42740