Theorem pm2.04 90

Description: Swap antecedents. Theorem *2.04 of [WhiteheadRussell] p. 100. This was the third axiom in Frege's logic system, specifically Proposition 8 of [Frege1879] p. 35. Its associated inference is com12 32. (Contributed by NM, 27-Dec-1992.) (Proof shortened by Wolf Lammen, 12-Sep-2012.)

Assertion

Ref	Expression
pm2.04	⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))

Proof of Theorem pm2.04

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → 𝜒)))
2	1	com23 86	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  com34  91  com45  97  bi2.04  391  merco2  1731  ralcom3  3363  bj-exalim  33958  syl5imp  40836  com3rgbi  40838  syl5impVD  41187  simplbi2comtVD  41212  19.41rgVD  41226  ax6e2eqVD  41231  adh-jarrsc  43226  adh-minim  43227  adh-minimp  43239  rexrsb  43288