Theorem ax11-pm 32819

Description: Proof of ax-11 2034 similar to PM's proof of alcom 2037 (PM*11.2). For a proof closer to PM's proof, see ax11-pm2 32823. Axiom ax-11 2034 is used in the proof only through nfa2 2040. (Contributed by BJ, 15-Sep-2018.) (Proof modification is discouraged.)

Assertion

Ref	Expression
ax11-pm	|- ( A. x A. y ph -> A. y A. x ph )

Proof of Theorem ax11-pm

Step	Hyp	Ref	Expression
1		2sp 2056	. . 3 |- ( A. x A. y ph -> ph )
2	1	gen2 1723	. 2 |- A. y A. x ( A. x A. y ph -> ph )
3		nfa2 2040	. . 3 |- F/ y A. x A. y ph
4		nfa1 2028	. . 3 |- F/ x A. x A. y ph
5	3, 4	2stdpc5 32816	. 2 |- ( A. y A. x ( A. x A. y ph -> ph ) -> ( A. x A. y ph -> A. y A. x ph ) )
6	2, 5	ax-mp 5	1 |- ( A. x A. y ph -> A. y A. x ph )

Syntax hints:   -> 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-or 385  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)