Theorem axc5c4c711toc4 38604

Description: Rederivation of axc4 2130 from axc5c4c711 38602. Note that only propositional calculus is required for the rederivation. (Contributed by Andrew Salmon, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
axc5c4c711toc4	|- ( A. x ( A. x ph -> ps ) -> ( A. x ph -> A. x ps ) )

Proof of Theorem axc5c4c711toc4

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 |- ( A. x ( A. x ph -> ps ) -> ( ph -> A. x ( A. x ph -> ps ) ) )
2		ax-1 6	. 2 |- ( ( ph -> A. x ( A. x ph -> ps ) ) -> ( A. x A. x -. A. x A. x ( A. x ph -> ps ) -> ( ph -> A. x ( A. x ph -> ps ) ) ) )
3		axc5c4c711 38602	. 2 |- ( ( A. x A. x -. A. x A. x ( A. x ph -> ps ) -> ( ph -> A. x ( A. x ph -> ps ) ) ) -> ( A. x ph -> A. x ps ) )
4	1, 2, 3	3syl 18	1 |- ( A. x ( A. x ph -> ps ) -> ( A. x ph -> A. x ps ) )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by: (None)