Theorem com13 80

Description: Commutation of antecedents. Swap 1st and 3rd. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)

Hypothesis

Ref	Expression
com3.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Assertion

Ref	Expression
com13	⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃)))

Proof of Theorem com13

Step	Hyp	Ref	Expression
1		com3.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2	1	com3r 79	. 2 ⊢ (𝜒 → (𝜑 → (𝜓 → 𝜃)))
3	2	com23 78	1 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  com24  87  an13s  567  an31s  570  3imp31  1196  3imp21  1198  funopg  5250  f1o2ndf1  6228  brecop  6624  fiintim  6927  elpq  9647  xnn0lenn0nn0  9864  elfz0ubfz0  10124  elfz0fzfz0  10125  fz0fzelfz0  10126  fz0fzdiffz0  10129  fzo1fzo0n0  10182  elfzodifsumelfzo  10200  ssfzo12  10223  ssfzo12bi  10224  facwordi  10719  fihashf1rn  10767  oddnn02np1  11884  oddge22np1  11885  evennn02n  11886  evennn2n  11887  dfgcd2  12014  sqrt2irr  12161  zabsle1  14370  bj-inf2vnlem2  14693