Theorem mooran1 1425

Description: "At most one" imports disjunction to conjunction.

Assertion

Ref	Expression
mooran1	|- ((E*xph \/ E*xps) -> E*x(ph /\ ps))

Proof of Theorem mooran1

Step	Hyp	Ref	Expression
1		moan 1422	. . 3 |- (E*xph -> E*x(ps /\ ph))
2		ancom 435	. . . 4 |- ((ps /\ ph) <-> (ph /\ ps))
3	2	mobii 1405	. . 3 |- (E*x(ps /\ ph) <-> E*x(ph /\ ps))
4	1, 3	sylib 198	. 2 |- (E*xph -> E*x(ph /\ ps))
5		moan 1422	. 2 |- (E*xps -> E*x(ph /\ ps))
6	4, 5	jaoi 341	1 |- ((E*xph \/ E*xps) -> E*x(ph /\ ps))

Syntax hints:   -> wi 3   \/ wo 222   /\ wa 223  E*wmo 1381

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-11 967  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-eu 1382  df-mo 1383

Copyright terms: Public domain