Theorem pm2.04 91

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 33. (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 23	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → 𝜒)))
2	1	com23 87	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  com34  92  com45  98  bi2.04  392  merco2  1769  spcimgft  3518  bj-almpi  37253  bj-exalim  37278  syl5imp  45262  com3rgbi  45264  syl5impVD  45612  simplbi2comtVD  45637  19.41rgVD  45651  ax6e2eqVD  45656  adh-jarrsc  47778  adh-minim  47779  adh-minimp  47791  rexrsb  47878