Theorem wl-pm2.04 33267

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. Copy of pm2.04 90 with a different proof. (Contributed by Wolf Lammen, 7-Jul-2019.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
wl-pm2.04	|- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> ch ) ) )

Proof of Theorem wl-pm2.04

Step	Hyp	Ref	Expression
1		wl-ax1 33256	. 2 |- ( ps -> ( ph -> ps ) )
2		wl-ax2 33264	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )
3	1, 2	wl-syl5 33247	1 |- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> ch ) ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 33241  ax-luk2 33242  ax-luk3 33243

This theorem is referenced by:  wl-impchain-com-1.2  33275  wl-impchain-com-1.3  33276  wl-impchain-com-1.4  33277