Theorem ifid 2347

Description: Identical true and false arguments in the conditional operator.

Assertion

Ref	Expression
ifid	|- if(ph, A, A) = A

Proof of Theorem ifid

Step	Hyp	Ref	Expression
1		iftrue 2337	. 2 |- (ph -> if(ph, A, A) = A)
2		iffalse 2338	. 2 |- (-. ph -> if(ph, A, A) = A)
3	1, 2	pm2.61i 126	1 |- if(ph, A, A) = A

Syntax hints:   = wceq 1099  ifcif 2332

This theorem is referenced by:  supsn 4515  metxptval 7718  metxp 7722

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-6 953  ax-7 954  ax-gen 955  ax-8 1101  ax-9 1102  ax-10 1103  ax-12 1104  ax-17 1190  ax-16 1194  ax-11o 1202  ax-ext 1436

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 957  df-sb 1155  df-clab 1441  df-cleq 1446  df-clel 1449  df-if 2333

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