Theorem excomw

Description: Weak version of excom and biconditional form of excomimw . Uses only Tarski's FOL axiom schemes. (Contributed by TM, 24-Jan-2026)

	Ref	Expression
Hypotheses	excomw.1	|- ( x = w -> ( ph <-> ps ) )
	excomw.2	|- ( y = z -> ( ph <-> ch ) )
Assertion	excomw	|- ( E. x E. y ph <-> E. y E. x ph )

Proof

Step	Hyp	Ref	Expression
1		excomw.1	|- ( x = w -> ( ph <-> ps ) )
2		excomw.2	|- ( y = z -> ( ph <-> ch ) )
3	1	excomimw	|- ( E. x E. y ph -> E. y E. x ph )
4	2	excomimw	|- ( E. y E. x ph -> E. x E. y ph )
5	3 4	impbii	|- ( E. x E. y ph <-> E. y E. x ph )